Interpretations of the Growth of Knowledge in Interpretations of the Growth of Knowledge in Dynamic Learning SituationsDynamic Learning Situations
Andraacutes BenedekAndraacutes BenedekInst of Philosophy Research Centre for the Humanities HAS
Cranach Tree of Knowledge (1472) benedekwebmailphil-insthu
Motto ldquoIf you have an idea and I have an idea and we exchange these ideas
then will each of us have two ideashelliprdquo (After GB Show)
A Plausible Thesis
Motivation
A common assumption lurking behind the debates of the 60ies
If you have an apple and I have an apple and we exchange apples then you and I will still each have one apple If you have an apple and I have an apple and we exchange apples then you and I will still each have one apple But if you have an idea and I have an idea and we exchange these ideas then each of us will have two ideasBut if you have an idea and I have an idea and we exchange these ideas then each of us will have two ideas
KKnowledge does grow as a result of collaboration and information exchangenowledge does grow as a result of collaboration and information exchange
Attributed to GB Show
Trivial (local) counterexamples
hellipto (re)interpret the bdquo bdquoGrowth of Knowledgerdquo rdquo in dynamic (logical) terms
Good old-fashioned Questions(to be reconsidered)
bull What is it that is growingndash What constitutes knowledgendash What kinds of knowledge are growingndash What exactly is lsquogrowingrsquo (if anything)
in case of the different types of knowledge bull What is lsquoGrowthrsquo
ndash What do we mean by (the) lsquogrowthrsquo (of knowledge)ndash What does lsquogrowthrsquo consist of
bull How is it measured ndash How do we detect growth (Triggers Statistics Indicators)ndash How do we represent growth (Orderings Patterns Measures)
bull How could the lsquomechanicsrsquo of growth processes be described ndash Temporal dynamics of learningndash What kind of dynamic models we have for the description of changes in epistemic states as growth of knowledge
Does Human Knowledge double in every 5gt3gthellip y
ears
What is growing Knowledge in bdquoobject(tive)rdquo forms (Books Data Stores Wikis
Scientific Journals Papers Cross References etc) The lsquoThird Worldrsquo (Sets of Propositions Problems Theories
Models Proofs Methodshellip) The Fields of inquiry (New Questions Subjects Frameworks) Knowledge collectives (Shared understandings Reflection
Awareness Common (Global) Knowledge
Knowledge in bdquoobject(tive)rdquo forms (Books Data Stores Wikis Scientific Journals Papers Cross References etc)
The lsquoThird Worldrsquo (Sets of Propositions Problems Theories Models Proofs Methodshellip)
The Fields of inquiry (New Questions Subjects Frameworks) Knowledge collectives (Shared understandings Reflection
Awareness Common (Global) Knowledge
What kind of knowledge
Theoretical
Tacit Propositional
Empirical
Organizational InstitutionalSocial
Procedural Strategic Methodological
What constitutes knowledge
-Types ofTypes of propositional(ly based) knowledgepropositional(ly based) knowledge
Individual Single-agentMulti-agent
Factual HypoteticalNormativ
Collective DistributedGroup CommonKnowledge Networks
ExplicitImplicit
--Conceptions of knowledgeConceptions of knowledgendashTheoretically grounded accumulating evidence Warranted belief
ndashJustified True Belief
ndashDefeasableUndefeasible knowledge
ndashPerceptual (enactive) knowledge etcndashAny piece of information that promotes the solution of a task (AI)
Reflexive MutualHigher Orderhellip
What kind of knowledge
What is lsquoGrowthrsquo What does Growth consist of How is it measured
Closeness Convergence to the truth
Changes in Relations bw Theories and Models Theory change
More people know it of KnowersOrganizationsCoPNetworks
Higher Degree of Belief Plausibility
Higher levels of reflexivity
Increase in truthlikenessverisimiltudefactual content etc
Higher Measure of Probability Utility
Elimination of possibilities possible worlds uncertainity
Inductive generalization
Dynamics of learningChanges in knowledge states are triggered by
bull incoming semantic information andbull epistemic action(s) including bull higher order reflection on the knowledge states of
others
Formal description of the effects of semantic information on communicating agents require epistemic models of changechange in knowledge states (represented by logic structures)
Brookesrsquo lsquofundamental equationrsquo K[S] + ΔI = K[S + ΔS] ΔI changes K[S] to K[S + ΔS] where K[S + ΔS] is the changed knowledge structure ie
information modifiesmodifies knowledge statesstructures
Dynamic logic models of changing knowledge states as a result of
communication
A ldquoB do you have redrdquo BobldquoNordquo
bdquoDynamicsrdquo Temporal development of agentsrsquo knowledge states restricted by bdquorulesrdquo Labeled transition systems represented by graphs
Other typical examples lsquo100 prisoners and a light bulbrsquo lsquoRussian cardsrsquo etc
Epistemic Logics emerging from Hintikkarsquos Knowledge and Belief (1962) set the background of modeling
information flow AND knowledge in a common framework
model the effect of information as a dynamic processdynamic processUpdatesUpgradesRevisions
Various operations in Dynamic Epistemic Logic (DEL) represent the changes
Current issues Models of information flow describe meaningful interactions between agents as abstract models of ldquosocial softwaresocial softwarerdquo
Dynamic LDynamic Logic ogic MModels odels of of IInformation nformation EExchangexchange
Tools for Modeling Growth
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Construction of semantic representations
Local epistemic states states of the the environment (shared statemens + public announcements eg)
Representation of communication protocols (eg in PAL)
Interpreted scenarios of information flow (transitions of knowledge)
Kripke structures in DEL
In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement
Epistemic Models
Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ
Group Knowledge
Combining individual knowledge to explicit Group Level
Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge
But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)
Group Knowledge and Full Communication
There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication
Their results can be extended to models equipped with specific communication structures
Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
A Plausible Thesis
Motivation
A common assumption lurking behind the debates of the 60ies
If you have an apple and I have an apple and we exchange apples then you and I will still each have one apple If you have an apple and I have an apple and we exchange apples then you and I will still each have one apple But if you have an idea and I have an idea and we exchange these ideas then each of us will have two ideasBut if you have an idea and I have an idea and we exchange these ideas then each of us will have two ideas
KKnowledge does grow as a result of collaboration and information exchangenowledge does grow as a result of collaboration and information exchange
Attributed to GB Show
Trivial (local) counterexamples
hellipto (re)interpret the bdquo bdquoGrowth of Knowledgerdquo rdquo in dynamic (logical) terms
Good old-fashioned Questions(to be reconsidered)
bull What is it that is growingndash What constitutes knowledgendash What kinds of knowledge are growingndash What exactly is lsquogrowingrsquo (if anything)
in case of the different types of knowledge bull What is lsquoGrowthrsquo
ndash What do we mean by (the) lsquogrowthrsquo (of knowledge)ndash What does lsquogrowthrsquo consist of
bull How is it measured ndash How do we detect growth (Triggers Statistics Indicators)ndash How do we represent growth (Orderings Patterns Measures)
bull How could the lsquomechanicsrsquo of growth processes be described ndash Temporal dynamics of learningndash What kind of dynamic models we have for the description of changes in epistemic states as growth of knowledge
Does Human Knowledge double in every 5gt3gthellip y
ears
What is growing Knowledge in bdquoobject(tive)rdquo forms (Books Data Stores Wikis
Scientific Journals Papers Cross References etc) The lsquoThird Worldrsquo (Sets of Propositions Problems Theories
Models Proofs Methodshellip) The Fields of inquiry (New Questions Subjects Frameworks) Knowledge collectives (Shared understandings Reflection
Awareness Common (Global) Knowledge
Knowledge in bdquoobject(tive)rdquo forms (Books Data Stores Wikis Scientific Journals Papers Cross References etc)
The lsquoThird Worldrsquo (Sets of Propositions Problems Theories Models Proofs Methodshellip)
The Fields of inquiry (New Questions Subjects Frameworks) Knowledge collectives (Shared understandings Reflection
Awareness Common (Global) Knowledge
What kind of knowledge
Theoretical
Tacit Propositional
Empirical
Organizational InstitutionalSocial
Procedural Strategic Methodological
What constitutes knowledge
-Types ofTypes of propositional(ly based) knowledgepropositional(ly based) knowledge
Individual Single-agentMulti-agent
Factual HypoteticalNormativ
Collective DistributedGroup CommonKnowledge Networks
ExplicitImplicit
--Conceptions of knowledgeConceptions of knowledgendashTheoretically grounded accumulating evidence Warranted belief
ndashJustified True Belief
ndashDefeasableUndefeasible knowledge
ndashPerceptual (enactive) knowledge etcndashAny piece of information that promotes the solution of a task (AI)
Reflexive MutualHigher Orderhellip
What kind of knowledge
What is lsquoGrowthrsquo What does Growth consist of How is it measured
Closeness Convergence to the truth
Changes in Relations bw Theories and Models Theory change
More people know it of KnowersOrganizationsCoPNetworks
Higher Degree of Belief Plausibility
Higher levels of reflexivity
Increase in truthlikenessverisimiltudefactual content etc
Higher Measure of Probability Utility
Elimination of possibilities possible worlds uncertainity
Inductive generalization
Dynamics of learningChanges in knowledge states are triggered by
bull incoming semantic information andbull epistemic action(s) including bull higher order reflection on the knowledge states of
others
Formal description of the effects of semantic information on communicating agents require epistemic models of changechange in knowledge states (represented by logic structures)
Brookesrsquo lsquofundamental equationrsquo K[S] + ΔI = K[S + ΔS] ΔI changes K[S] to K[S + ΔS] where K[S + ΔS] is the changed knowledge structure ie
information modifiesmodifies knowledge statesstructures
Dynamic logic models of changing knowledge states as a result of
communication
A ldquoB do you have redrdquo BobldquoNordquo
bdquoDynamicsrdquo Temporal development of agentsrsquo knowledge states restricted by bdquorulesrdquo Labeled transition systems represented by graphs
Other typical examples lsquo100 prisoners and a light bulbrsquo lsquoRussian cardsrsquo etc
Epistemic Logics emerging from Hintikkarsquos Knowledge and Belief (1962) set the background of modeling
information flow AND knowledge in a common framework
model the effect of information as a dynamic processdynamic processUpdatesUpgradesRevisions
Various operations in Dynamic Epistemic Logic (DEL) represent the changes
Current issues Models of information flow describe meaningful interactions between agents as abstract models of ldquosocial softwaresocial softwarerdquo
Dynamic LDynamic Logic ogic MModels odels of of IInformation nformation EExchangexchange
Tools for Modeling Growth
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Construction of semantic representations
Local epistemic states states of the the environment (shared statemens + public announcements eg)
Representation of communication protocols (eg in PAL)
Interpreted scenarios of information flow (transitions of knowledge)
Kripke structures in DEL
In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement
Epistemic Models
Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ
Group Knowledge
Combining individual knowledge to explicit Group Level
Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge
But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)
Group Knowledge and Full Communication
There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication
Their results can be extended to models equipped with specific communication structures
Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Good old-fashioned Questions(to be reconsidered)
bull What is it that is growingndash What constitutes knowledgendash What kinds of knowledge are growingndash What exactly is lsquogrowingrsquo (if anything)
in case of the different types of knowledge bull What is lsquoGrowthrsquo
ndash What do we mean by (the) lsquogrowthrsquo (of knowledge)ndash What does lsquogrowthrsquo consist of
bull How is it measured ndash How do we detect growth (Triggers Statistics Indicators)ndash How do we represent growth (Orderings Patterns Measures)
bull How could the lsquomechanicsrsquo of growth processes be described ndash Temporal dynamics of learningndash What kind of dynamic models we have for the description of changes in epistemic states as growth of knowledge
Does Human Knowledge double in every 5gt3gthellip y
ears
What is growing Knowledge in bdquoobject(tive)rdquo forms (Books Data Stores Wikis
Scientific Journals Papers Cross References etc) The lsquoThird Worldrsquo (Sets of Propositions Problems Theories
Models Proofs Methodshellip) The Fields of inquiry (New Questions Subjects Frameworks) Knowledge collectives (Shared understandings Reflection
Awareness Common (Global) Knowledge
Knowledge in bdquoobject(tive)rdquo forms (Books Data Stores Wikis Scientific Journals Papers Cross References etc)
The lsquoThird Worldrsquo (Sets of Propositions Problems Theories Models Proofs Methodshellip)
The Fields of inquiry (New Questions Subjects Frameworks) Knowledge collectives (Shared understandings Reflection
Awareness Common (Global) Knowledge
What kind of knowledge
Theoretical
Tacit Propositional
Empirical
Organizational InstitutionalSocial
Procedural Strategic Methodological
What constitutes knowledge
-Types ofTypes of propositional(ly based) knowledgepropositional(ly based) knowledge
Individual Single-agentMulti-agent
Factual HypoteticalNormativ
Collective DistributedGroup CommonKnowledge Networks
ExplicitImplicit
--Conceptions of knowledgeConceptions of knowledgendashTheoretically grounded accumulating evidence Warranted belief
ndashJustified True Belief
ndashDefeasableUndefeasible knowledge
ndashPerceptual (enactive) knowledge etcndashAny piece of information that promotes the solution of a task (AI)
Reflexive MutualHigher Orderhellip
What kind of knowledge
What is lsquoGrowthrsquo What does Growth consist of How is it measured
Closeness Convergence to the truth
Changes in Relations bw Theories and Models Theory change
More people know it of KnowersOrganizationsCoPNetworks
Higher Degree of Belief Plausibility
Higher levels of reflexivity
Increase in truthlikenessverisimiltudefactual content etc
Higher Measure of Probability Utility
Elimination of possibilities possible worlds uncertainity
Inductive generalization
Dynamics of learningChanges in knowledge states are triggered by
bull incoming semantic information andbull epistemic action(s) including bull higher order reflection on the knowledge states of
others
Formal description of the effects of semantic information on communicating agents require epistemic models of changechange in knowledge states (represented by logic structures)
Brookesrsquo lsquofundamental equationrsquo K[S] + ΔI = K[S + ΔS] ΔI changes K[S] to K[S + ΔS] where K[S + ΔS] is the changed knowledge structure ie
information modifiesmodifies knowledge statesstructures
Dynamic logic models of changing knowledge states as a result of
communication
A ldquoB do you have redrdquo BobldquoNordquo
bdquoDynamicsrdquo Temporal development of agentsrsquo knowledge states restricted by bdquorulesrdquo Labeled transition systems represented by graphs
Other typical examples lsquo100 prisoners and a light bulbrsquo lsquoRussian cardsrsquo etc
Epistemic Logics emerging from Hintikkarsquos Knowledge and Belief (1962) set the background of modeling
information flow AND knowledge in a common framework
model the effect of information as a dynamic processdynamic processUpdatesUpgradesRevisions
Various operations in Dynamic Epistemic Logic (DEL) represent the changes
Current issues Models of information flow describe meaningful interactions between agents as abstract models of ldquosocial softwaresocial softwarerdquo
Dynamic LDynamic Logic ogic MModels odels of of IInformation nformation EExchangexchange
Tools for Modeling Growth
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Construction of semantic representations
Local epistemic states states of the the environment (shared statemens + public announcements eg)
Representation of communication protocols (eg in PAL)
Interpreted scenarios of information flow (transitions of knowledge)
Kripke structures in DEL
In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement
Epistemic Models
Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ
Group Knowledge
Combining individual knowledge to explicit Group Level
Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge
But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)
Group Knowledge and Full Communication
There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication
Their results can be extended to models equipped with specific communication structures
Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
What is growing Knowledge in bdquoobject(tive)rdquo forms (Books Data Stores Wikis
Scientific Journals Papers Cross References etc) The lsquoThird Worldrsquo (Sets of Propositions Problems Theories
Models Proofs Methodshellip) The Fields of inquiry (New Questions Subjects Frameworks) Knowledge collectives (Shared understandings Reflection
Awareness Common (Global) Knowledge
Knowledge in bdquoobject(tive)rdquo forms (Books Data Stores Wikis Scientific Journals Papers Cross References etc)
The lsquoThird Worldrsquo (Sets of Propositions Problems Theories Models Proofs Methodshellip)
The Fields of inquiry (New Questions Subjects Frameworks) Knowledge collectives (Shared understandings Reflection
Awareness Common (Global) Knowledge
What kind of knowledge
Theoretical
Tacit Propositional
Empirical
Organizational InstitutionalSocial
Procedural Strategic Methodological
What constitutes knowledge
-Types ofTypes of propositional(ly based) knowledgepropositional(ly based) knowledge
Individual Single-agentMulti-agent
Factual HypoteticalNormativ
Collective DistributedGroup CommonKnowledge Networks
ExplicitImplicit
--Conceptions of knowledgeConceptions of knowledgendashTheoretically grounded accumulating evidence Warranted belief
ndashJustified True Belief
ndashDefeasableUndefeasible knowledge
ndashPerceptual (enactive) knowledge etcndashAny piece of information that promotes the solution of a task (AI)
Reflexive MutualHigher Orderhellip
What kind of knowledge
What is lsquoGrowthrsquo What does Growth consist of How is it measured
Closeness Convergence to the truth
Changes in Relations bw Theories and Models Theory change
More people know it of KnowersOrganizationsCoPNetworks
Higher Degree of Belief Plausibility
Higher levels of reflexivity
Increase in truthlikenessverisimiltudefactual content etc
Higher Measure of Probability Utility
Elimination of possibilities possible worlds uncertainity
Inductive generalization
Dynamics of learningChanges in knowledge states are triggered by
bull incoming semantic information andbull epistemic action(s) including bull higher order reflection on the knowledge states of
others
Formal description of the effects of semantic information on communicating agents require epistemic models of changechange in knowledge states (represented by logic structures)
Brookesrsquo lsquofundamental equationrsquo K[S] + ΔI = K[S + ΔS] ΔI changes K[S] to K[S + ΔS] where K[S + ΔS] is the changed knowledge structure ie
information modifiesmodifies knowledge statesstructures
Dynamic logic models of changing knowledge states as a result of
communication
A ldquoB do you have redrdquo BobldquoNordquo
bdquoDynamicsrdquo Temporal development of agentsrsquo knowledge states restricted by bdquorulesrdquo Labeled transition systems represented by graphs
Other typical examples lsquo100 prisoners and a light bulbrsquo lsquoRussian cardsrsquo etc
Epistemic Logics emerging from Hintikkarsquos Knowledge and Belief (1962) set the background of modeling
information flow AND knowledge in a common framework
model the effect of information as a dynamic processdynamic processUpdatesUpgradesRevisions
Various operations in Dynamic Epistemic Logic (DEL) represent the changes
Current issues Models of information flow describe meaningful interactions between agents as abstract models of ldquosocial softwaresocial softwarerdquo
Dynamic LDynamic Logic ogic MModels odels of of IInformation nformation EExchangexchange
Tools for Modeling Growth
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Construction of semantic representations
Local epistemic states states of the the environment (shared statemens + public announcements eg)
Representation of communication protocols (eg in PAL)
Interpreted scenarios of information flow (transitions of knowledge)
Kripke structures in DEL
In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement
Epistemic Models
Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ
Group Knowledge
Combining individual knowledge to explicit Group Level
Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge
But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)
Group Knowledge and Full Communication
There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication
Their results can be extended to models equipped with specific communication structures
Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
What constitutes knowledge
-Types ofTypes of propositional(ly based) knowledgepropositional(ly based) knowledge
Individual Single-agentMulti-agent
Factual HypoteticalNormativ
Collective DistributedGroup CommonKnowledge Networks
ExplicitImplicit
--Conceptions of knowledgeConceptions of knowledgendashTheoretically grounded accumulating evidence Warranted belief
ndashJustified True Belief
ndashDefeasableUndefeasible knowledge
ndashPerceptual (enactive) knowledge etcndashAny piece of information that promotes the solution of a task (AI)
Reflexive MutualHigher Orderhellip
What kind of knowledge
What is lsquoGrowthrsquo What does Growth consist of How is it measured
Closeness Convergence to the truth
Changes in Relations bw Theories and Models Theory change
More people know it of KnowersOrganizationsCoPNetworks
Higher Degree of Belief Plausibility
Higher levels of reflexivity
Increase in truthlikenessverisimiltudefactual content etc
Higher Measure of Probability Utility
Elimination of possibilities possible worlds uncertainity
Inductive generalization
Dynamics of learningChanges in knowledge states are triggered by
bull incoming semantic information andbull epistemic action(s) including bull higher order reflection on the knowledge states of
others
Formal description of the effects of semantic information on communicating agents require epistemic models of changechange in knowledge states (represented by logic structures)
Brookesrsquo lsquofundamental equationrsquo K[S] + ΔI = K[S + ΔS] ΔI changes K[S] to K[S + ΔS] where K[S + ΔS] is the changed knowledge structure ie
information modifiesmodifies knowledge statesstructures
Dynamic logic models of changing knowledge states as a result of
communication
A ldquoB do you have redrdquo BobldquoNordquo
bdquoDynamicsrdquo Temporal development of agentsrsquo knowledge states restricted by bdquorulesrdquo Labeled transition systems represented by graphs
Other typical examples lsquo100 prisoners and a light bulbrsquo lsquoRussian cardsrsquo etc
Epistemic Logics emerging from Hintikkarsquos Knowledge and Belief (1962) set the background of modeling
information flow AND knowledge in a common framework
model the effect of information as a dynamic processdynamic processUpdatesUpgradesRevisions
Various operations in Dynamic Epistemic Logic (DEL) represent the changes
Current issues Models of information flow describe meaningful interactions between agents as abstract models of ldquosocial softwaresocial softwarerdquo
Dynamic LDynamic Logic ogic MModels odels of of IInformation nformation EExchangexchange
Tools for Modeling Growth
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Construction of semantic representations
Local epistemic states states of the the environment (shared statemens + public announcements eg)
Representation of communication protocols (eg in PAL)
Interpreted scenarios of information flow (transitions of knowledge)
Kripke structures in DEL
In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement
Epistemic Models
Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ
Group Knowledge
Combining individual knowledge to explicit Group Level
Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge
But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)
Group Knowledge and Full Communication
There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication
Their results can be extended to models equipped with specific communication structures
Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
What is lsquoGrowthrsquo What does Growth consist of How is it measured
Closeness Convergence to the truth
Changes in Relations bw Theories and Models Theory change
More people know it of KnowersOrganizationsCoPNetworks
Higher Degree of Belief Plausibility
Higher levels of reflexivity
Increase in truthlikenessverisimiltudefactual content etc
Higher Measure of Probability Utility
Elimination of possibilities possible worlds uncertainity
Inductive generalization
Dynamics of learningChanges in knowledge states are triggered by
bull incoming semantic information andbull epistemic action(s) including bull higher order reflection on the knowledge states of
others
Formal description of the effects of semantic information on communicating agents require epistemic models of changechange in knowledge states (represented by logic structures)
Brookesrsquo lsquofundamental equationrsquo K[S] + ΔI = K[S + ΔS] ΔI changes K[S] to K[S + ΔS] where K[S + ΔS] is the changed knowledge structure ie
information modifiesmodifies knowledge statesstructures
Dynamic logic models of changing knowledge states as a result of
communication
A ldquoB do you have redrdquo BobldquoNordquo
bdquoDynamicsrdquo Temporal development of agentsrsquo knowledge states restricted by bdquorulesrdquo Labeled transition systems represented by graphs
Other typical examples lsquo100 prisoners and a light bulbrsquo lsquoRussian cardsrsquo etc
Epistemic Logics emerging from Hintikkarsquos Knowledge and Belief (1962) set the background of modeling
information flow AND knowledge in a common framework
model the effect of information as a dynamic processdynamic processUpdatesUpgradesRevisions
Various operations in Dynamic Epistemic Logic (DEL) represent the changes
Current issues Models of information flow describe meaningful interactions between agents as abstract models of ldquosocial softwaresocial softwarerdquo
Dynamic LDynamic Logic ogic MModels odels of of IInformation nformation EExchangexchange
Tools for Modeling Growth
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Construction of semantic representations
Local epistemic states states of the the environment (shared statemens + public announcements eg)
Representation of communication protocols (eg in PAL)
Interpreted scenarios of information flow (transitions of knowledge)
Kripke structures in DEL
In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement
Epistemic Models
Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ
Group Knowledge
Combining individual knowledge to explicit Group Level
Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge
But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)
Group Knowledge and Full Communication
There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication
Their results can be extended to models equipped with specific communication structures
Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Dynamics of learningChanges in knowledge states are triggered by
bull incoming semantic information andbull epistemic action(s) including bull higher order reflection on the knowledge states of
others
Formal description of the effects of semantic information on communicating agents require epistemic models of changechange in knowledge states (represented by logic structures)
Brookesrsquo lsquofundamental equationrsquo K[S] + ΔI = K[S + ΔS] ΔI changes K[S] to K[S + ΔS] where K[S + ΔS] is the changed knowledge structure ie
information modifiesmodifies knowledge statesstructures
Dynamic logic models of changing knowledge states as a result of
communication
A ldquoB do you have redrdquo BobldquoNordquo
bdquoDynamicsrdquo Temporal development of agentsrsquo knowledge states restricted by bdquorulesrdquo Labeled transition systems represented by graphs
Other typical examples lsquo100 prisoners and a light bulbrsquo lsquoRussian cardsrsquo etc
Epistemic Logics emerging from Hintikkarsquos Knowledge and Belief (1962) set the background of modeling
information flow AND knowledge in a common framework
model the effect of information as a dynamic processdynamic processUpdatesUpgradesRevisions
Various operations in Dynamic Epistemic Logic (DEL) represent the changes
Current issues Models of information flow describe meaningful interactions between agents as abstract models of ldquosocial softwaresocial softwarerdquo
Dynamic LDynamic Logic ogic MModels odels of of IInformation nformation EExchangexchange
Tools for Modeling Growth
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Construction of semantic representations
Local epistemic states states of the the environment (shared statemens + public announcements eg)
Representation of communication protocols (eg in PAL)
Interpreted scenarios of information flow (transitions of knowledge)
Kripke structures in DEL
In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement
Epistemic Models
Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ
Group Knowledge
Combining individual knowledge to explicit Group Level
Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge
But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)
Group Knowledge and Full Communication
There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication
Their results can be extended to models equipped with specific communication structures
Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Dynamic logic models of changing knowledge states as a result of
communication
A ldquoB do you have redrdquo BobldquoNordquo
bdquoDynamicsrdquo Temporal development of agentsrsquo knowledge states restricted by bdquorulesrdquo Labeled transition systems represented by graphs
Other typical examples lsquo100 prisoners and a light bulbrsquo lsquoRussian cardsrsquo etc
Epistemic Logics emerging from Hintikkarsquos Knowledge and Belief (1962) set the background of modeling
information flow AND knowledge in a common framework
model the effect of information as a dynamic processdynamic processUpdatesUpgradesRevisions
Various operations in Dynamic Epistemic Logic (DEL) represent the changes
Current issues Models of information flow describe meaningful interactions between agents as abstract models of ldquosocial softwaresocial softwarerdquo
Dynamic LDynamic Logic ogic MModels odels of of IInformation nformation EExchangexchange
Tools for Modeling Growth
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Construction of semantic representations
Local epistemic states states of the the environment (shared statemens + public announcements eg)
Representation of communication protocols (eg in PAL)
Interpreted scenarios of information flow (transitions of knowledge)
Kripke structures in DEL
In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement
Epistemic Models
Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ
Group Knowledge
Combining individual knowledge to explicit Group Level
Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge
But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)
Group Knowledge and Full Communication
There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication
Their results can be extended to models equipped with specific communication structures
Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Epistemic Logics emerging from Hintikkarsquos Knowledge and Belief (1962) set the background of modeling
information flow AND knowledge in a common framework
model the effect of information as a dynamic processdynamic processUpdatesUpgradesRevisions
Various operations in Dynamic Epistemic Logic (DEL) represent the changes
Current issues Models of information flow describe meaningful interactions between agents as abstract models of ldquosocial softwaresocial softwarerdquo
Dynamic LDynamic Logic ogic MModels odels of of IInformation nformation EExchangexchange
Tools for Modeling Growth
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Construction of semantic representations
Local epistemic states states of the the environment (shared statemens + public announcements eg)
Representation of communication protocols (eg in PAL)
Interpreted scenarios of information flow (transitions of knowledge)
Kripke structures in DEL
In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement
Epistemic Models
Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ
Group Knowledge
Combining individual knowledge to explicit Group Level
Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge
But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)
Group Knowledge and Full Communication
There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication
Their results can be extended to models equipped with specific communication structures
Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Tools for Modeling Growth
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information
Group level revision induced by communication between members of the group
Assumptions eg sincerity members already accept the information (before sharing it)
Higher-level (doxastic) information may refer to the
agents own beliefs or even to their belief-revision plans
Construction of semantic representations
Local epistemic states states of the the environment (shared statemens + public announcements eg)
Representation of communication protocols (eg in PAL)
Interpreted scenarios of information flow (transitions of knowledge)
Kripke structures in DEL
In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement
Epistemic Models
Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ
Group Knowledge
Combining individual knowledge to explicit Group Level
Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge
But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)
Group Knowledge and Full Communication
There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication
Their results can be extended to models equipped with specific communication structures
Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Construction of semantic representations
Local epistemic states states of the the environment (shared statemens + public announcements eg)
Representation of communication protocols (eg in PAL)
Interpreted scenarios of information flow (transitions of knowledge)
Kripke structures in DEL
In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement
Epistemic Models
Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ
Group Knowledge
Combining individual knowledge to explicit Group Level
Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge
But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)
Group Knowledge and Full Communication
There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication
Their results can be extended to models equipped with specific communication structures
Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement
Epistemic Models
Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ
Group Knowledge
Combining individual knowledge to explicit Group Level
Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge
But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)
Group Knowledge and Full Communication
There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication
Their results can be extended to models equipped with specific communication structures
Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ
Group Knowledge
Combining individual knowledge to explicit Group Level
Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge
But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)
Group Knowledge and Full Communication
There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication
Their results can be extended to models equipped with specific communication structures
Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Group Knowledge
Combining individual knowledge to explicit Group Level
Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge
But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)
Group Knowledge and Full Communication
There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication
Their results can be extended to models equipped with specific communication structures
Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Combining individual knowledge to explicit Group Level
Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge
But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)
Group Knowledge and Full Communication
There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication
Their results can be extended to models equipped with specific communication structures
Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Group Knowledge and Full Communication
There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication
Their results can be extended to models equipped with specific communication structures
Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Communication Structures
Communication graphs
Relational algebras
Galois lattices
Hyper graphs
CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures
Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)
NB Applications to social networks
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Communication Protocols(CP)
Eg
Security policies Secrecy
Rules for making private information public
Sincerity conditions
Orders of epistemic actions communications temporal or historical possibilities
Restrictions eg only (hard) factual information is communicated
Soft (eg communicated non-reliable) information is allowed
Higher order epistemic information is communicatedrestricted
Bounds on levels of Reflection
RulesRegulationsPatternsProcedures that govern knowledge transfer
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Communication Protocols in DELCommunication Protocols in DEL
Freedom of SpeechNo Hiding
Telling the Truth
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions
The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Schematic validities
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Common KnowledgeCommon Knowledge
DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know
For common knowledge you have to compute the transitive closure of the union of the accessibility relations
A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Problems
Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities
bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade
Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment
Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Upgrades
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Upgrades that may represent Growth
Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision
Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Our kknowledgenowledgeRR of what the others know depends on
CP
CS
Ki(CS)
Dependencies of Reflexive KKnowledgenowledge(K(KRR))
Synchronous communication = message sent to a whole group
Asynchronous communication = message sent in serialtemporal order
Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo
There are formulas that the agents may come to know that are not explicitly contained in their communications
Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
Thank youThank you Thank youThank you
QuestionsQuestions CommentsComments
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216
ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216