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Knowledge Representation

CS 171/CS 271

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How to represent reality? Use an ontology (a formal

representation of reality) General/abstract domain Specific domains

Goal is to incorporate an ontology in a computer system such that the system seems to know the domain

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Using Logic forKnowledge Representation Propositional and First-Order Logic

describe the technology for knowledge-based agents

What gets into these knowledge bases? Categories, objects, substances Agent actions, situations, events Beliefs Uncertain information Dynamic information

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Categories Intelligent system -> a system that

seems to “reason” Human reasoning is based largely on

categories Presence of a certain object from perceptual

input Category membership inferred from

perceived properties Predictions can be made about that said

object

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Categories Example:

You observe the presence of a certain something (perceptual input)

Green, mottled skin, large size, ovoid shape (perceived properties from perceptual input)

Conclusion: that something is a Watermelon Watermelon is a fruit Prediction? Watermelon is good for fruit

salad

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Categories Example:

You observe the presence of a certain something (perceptual input)

Average height, brown skin, familiar hair, Dardar shape (perceived properties from perceptual input)

Conclusion: that something is Dardar Dardar is a friend Dardar is a good choice to ask food

from

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Categories Test:

Is there a difference between property and category?

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Categories Representing categories

As predicates: Singer( Madonna) As objects: Member( Madonna,

Singers ) or Madonna Singers

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Categories Basketball(b) Member(b,Basketball)

b Basketball Subset(Basketballs, Balls)

Balls Basketballs

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Categories A category being a set of its

members A complex object that has Member

and Subset relations defined to it

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Categories To simplify the knowledge base,

inheritance may be used whenever applicable

Inheritance in objects involving categories Think of inheritance in object oriented

programing What examples of inheritance can

you think of?

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Categories Related notions

Subclasses/subcategories ( ) Categories versus properties Categories of categories

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Relationships between Categories Disjoint categories Exhaustive decomposition Partition

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Relationships between Categories Disjoint categories

No members in common Exhaustive decomposition

If not a member of one, must be a member of the other

Partition A disjoint exhaustive decomposition

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Relationships between Categories Disjoint categories

Disjoint( {Animals, Vegetables} ) Exhaustive decomposition

ExhaustiveDecomposition( {Faculty,Staff,Administrators}, UniversityPersonnel )

Partition Partition( {Males,Females}, Persons )

Look at the white board

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Physical Composition Part-of relationship Composite objects

With structural properties (e.g., car as something with wheels and other things attached to it)

Transitive and Reflexive Look at the white board

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Physical Composition “The apples in the bag weigh 2

pounds” Weight of 2 pounds ascribed to a set

of apples – is this the correct way? Set is an abstract mathematical concept

with elements , but not weight Concept of the BUNCH

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Physical Composition BunchOf( {Apple1, Apple2,

Apple3} ) BunchOf(Apples) BunchOf(Apples) vs. Apples

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Measurements Measures as objects Measure: a number with units Example

Length(L1) = Inches(1.5)

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Measurements Diamater(Basketball) = Inches(9.5) LastPrice(Basketball) = $(19) d Days -> Duration(d) =

Hours(24)

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Measurements Inches(0) vs. Centimeters(0) vs.

Seconds(0) Note differences in what they

represent

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Measurements Measures are easy if they are

quantitative How about qualitative

measurements? Assign quantities to qualitative

concepts? Is this the correct/best way?

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Measurements Quantifying non numerical measures

Unnecessary! Imagine imposing a numerical scale on

beauty An important aspect of measures is

not the particular numerical values but the fact that the measures can be ordered What does this mean?

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Substances and Objects x Butter PartOf( y,x ) y

Butter This is true

x Dog PartOf( y,x ) y Dog Is this true?

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Substances and Objects Slice butter in 2, you get 2 tangible

objects, both are butter Slice a dog in 2, what do you get? Illustrates 2 important concepts:

STUFF THING

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Substances and Objects World not necessarily

individuated Not always divided into distinct

objects In the English language

Count nouns versus mass nouns

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Actions In the context of an agent, we need

to represent actions and consequences

Need to also worry about percepts, time, changing situations, and many others

Situation calculus or event calculus

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Situation Calculus Situations Fluents Eternal Predicates

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Situation Calculus Situations

Logical terms consisting of the initial situation S0 and all situations generated by applying an action to a situation

Objects/terms that stand for the states between actions carried out (initial situation and generated situations after an action)

Result( a, s ) names the resulting state when action a is executed in situation s

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Situation Calculus Fluents

Predicates/functions that vary across situations

Holding(G1, S0 ) Age( Dardar, S3 )

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Actions in Situation Calculus Possibility Axiom

It is possible to execute an action Effect Axiom

What happens when a possible action is executed

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Actions in Situation Calculus Possibility Axiom

preconditions Poss( action, situation ) Example:

“can move to a square if it is adjacent” “can feed Dardar if Dardar is hungry”

Effect Axiom Poss( action, situation ) changes Example:

“moving updates agent position”“Feeding Dardar makes Dardar not hungry”

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Frame Problem In the real world, most things stay the

same from one situation to the next Change occurs for a tiny fraction of the

fluents Note: effect action would often only note

those changes Frame problem: problem of representing

those that stay the same Efficiency/compactness issue Representational versus Inferential

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Inadequacy of Situation Calculus

Situation Calculus works well with Single agent involved Actions are discrete

What if: Not dealing with a single agent Actions have duretion and may

overlap across situations

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Event Calculus Based on points in time instead of

situations Time as objects Fluents hold at points in time Reasoning can be made over time

intervals (more humanlike!) More next week

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Other Challenges Beliefs Uncertain Information Dynamic Information