D. Calvanese, E. Kharlamov,W. Nutt, and D. Zheleznyakov

Free University of Bozen-Bolzano

ISWC, ShanghaiNovember, 2010

Evolution of DL-Lite Knowledge Bases

Description Logics (DLs)

Cleric

Priest

HusbandConcepts are classes of objects

Roles are relations between objects

TBox is for structure of the knowledge

ABox isfor instances of concepts and roles

CarlJohn

Adam

Bob

DL Knowledge Base:

TBox:

ABox:

This is a formalism underlying ontologies2/31

Knowledge Base

Single Husband

Priest

Wife

hasHb

Concepts:

Roles:

TBox:

ABox:

Wife, Husband, Single, Woman, PriestHasHb

Wife Woman ⊑Wife ≡ HasHb∃Husband ≡ HasHb∃ –

Husband ¬ Single⊑Priest Single⊑Husband ¬ Priest⊑

Wife(Mary), hasHb(Mary,John)Priest(Adam), Priest(Bob)

Woman

Mary

John

Adam Bob

(Mary, John)

1..n

1..n

3/31

What if There Is New Information?

Single Husband

Priest

Wife

hasHb

New Inormation N:

Single(John)

How should the KB evolve?

Woman

Mary

John

Adam Bob

(Mary, John)

1..n

1..n

John

4/31

DLs and Semantic Web

Ontology Web Language (OWL) is W3C recommendation for SWDLs provide foundation for OWL

DL-Lite: tractable fragment of DLPTime reasoningessentially Horn Logictractable profile of OWL 2 QL

5/31

Why Is Evolution Interesting?

Application domains are modeled usingOntologies/OWLThe state of the domain changeNew facts about domain appear

Web Services change information represented through OntologiesHow does the Ontology change?

6/31

Outline

I. Requirements for an evolution operatorII. Attempt to apply classical approaches

a) Model-Based approachesb) Formula-Based approaches

III. Our proposala) Bold Semanticsb) Careful Semantics

IV. Conclusion

Conceptual Requirements

Single Husband

John

RentSub

Wife

Mary

hasHb

1..n

Cleric

Minister

Carl

PriestAdam Bob

Single Husband

John

Cleric

Minister

Carl

RentSub

PriestAdam Bob

Wife

Mary

hasHb

1..n

Old Knowledge: New Knowledge: Evolved Knowledge:

DL-Lite KB Evolution Operator DL-Lite KBEvolved knowledge should be consistent – no logical contradictions be coherent – no empty concepts entail New Knowledge minimally different from the old KB – principle of minimal change

Priest(Bob)∧¬Priest(Bob) Priest Single⊑Priest ¬Single⊑

8/31

Technical Requirements

Closure under evolution:Evolution result should be expressible in DL-Lite

Efficiency:Evolution result should be computable in PTime

9/31

Can Previous Work Help?

Knowledge evolution was studied by the AI community

Primarily for Propositional Logic (PL)

Two main types of approaches to evolution in PL:1. Model-Based Approaches (MBAs)

operate with set of models2. Formula-Based Approaches (FBAs)

operate with set of formulas

Which of them are applicable to DL-Lite evolution?

10/31

Outline

I. Requirements for an evolution operatorII. Attempt to apply classical approaches

a) Model-Based approachesb) Formula-Based approaches

III. Our proposala) Bold Semanticsb) Careful Semantics

IV. Conclusion

Model-Based Approaches

Single Husband

John

RentSub

Wife

Mary

hasHb

1..n

Old Knowledge K:

Cleric

Minister

Carl

PriestAdam Bob

New Knowledge N:

Mod(K)

Mod(N)

Mod(N) are too many models

Keep those that are “closest” to Mod(K)

Two flavours of Model-Based Approaches: •Local•Global

12/31

Local Model-Based Approaches

Single Husband

John

RentSub

Wife

Mary

hasHb

1..n

Old Knowledge K:

Cleric

Minister

Carl

PriestAdam Bob

New Knowledge N:

Mod(K)

Mod(N)

The result of evolution:

Minimaldistance

Minimaldistance

Minimaldistance

Minimaldistance

13/31

Local Model-Based Approaches

Single Husband

John

RentSub

Wife

Mary

hasHb

1..n

Mod(K)

Mod(K’)

The result of evolution:Single Husba

nd

John

Cleric

MinisterCarl

RentSub

PriestAdam Bob

WifeMary

hasHb

1..n

Is there a representation?

Old Knowledge K:

Evolved KB K’:

13/31

Global Model-Based ApproachesOld Knowledge K:

Cleric

Minister

Carl

PriestAdam Bob

New Knowledge N:

Mod(K)

Mod(N)

The result of evolution:

Single Husband

John

RentSub

Wife

Mary

hasHb

1..n

14/31

Global Model-Based Approaches

Single Husband

John

RentSub

Wife

Mary

hasHb

1..n

Mod(K)

Mod(K’)

The result of evolution:Single Husba

nd

John

Cleric

MinisterCarl

RentSub

PriestAdam Bob

WifeMary

hasHb

1..n

Is there a representation?

Old Knowledge K:

Evolved KB K’:

14/31

How to Measure Distance btw Models?

All MBAs are based ondistances between interpretations

Distance in Propositional Logic:as a setas a number

Example:I = {p, q, r}J = {p, s}

dist⊖(I,J) = I ⊖ Jdist|⊖| (I,J) = |I ⊖ J|

dist⊖(I,J) = {q, r, s}

dist|⊖| (I,J) = 3

15/31

Dimensions of MBAsApproach

What is distance

Distance is built upon

set: ⊖ number: |⊖|

global: G

local: L

symbols: S

atoms: A

Propositional Logic: two dimensions. Description Logics: one more dimension!

Distance is built upon• symbols• atoms

16/31

Dimensions of MBAsApproach

What is distance

Distance is built upon

set: ⊖ number: |⊖|

global: G

local: L

symbols: S

atoms: A

Example:I = {Priest(Bob), Wife(Mary)}, J = {Priest(Adam), Wife(Mary)}

• Atoms: dist⊖(I,J) = {Priest(Bob), Priest(Adam)}

• Symbols: dist⊖(I,J) = {Priest}

16/31

Dimensions of MBAsApproach

What is distance

Distance is built upon

set: ⊖ number: |⊖|

global: G

local: L

symbols: S

atoms: A

Two possibilities for each of three dimensions eight possible semantics

Inexpressibility Theorem:• For all of eight semantics the result of the evolution

cannot be expressed in DL-Lite16/31

What May Go Wrong?Single Husband

Priest

Wife

hasHb

1..n

MBAs give more cases:3. Mary is married to either Adam or Bob (but not to both)

John

Adam Bob

a guyNew Knowledge: Single(John)

What happened with Mary?

Our intuition: 2 cases1. Mary is single 2. Mary is married to another guy

Drawback I: Mary married to one of the priest is counterintuitive

K’ Priest(Bob)⊭K’ Priest(Adam)⊭K’ Priest(Adam) ⊨ ∨ Priest(Bob)

Drawback II: Inexpressible in DL-Lite

WomanMary

1..n

(Mary, John )?

17/31

MBAs Do Not Work

… becausethey ignore structure of the KBthe allow too many casesresult of evolution cannot be expressed in DL-Lite

MBAs cannot be adopted for KB evolution in DL-Lite

18/31

Outline

I. Requirements for an evolution operatorII. Attempt to apply classical approaches

a) Model-Based approachesb) Formula-Based approaches

III. Our proposala) Bold Semanticsb) Careful Semantics

IV. Conclusion

Formula-Based Approaches

Idea:To take union K ∪ N

What if K ∪ N is unsatisfiable?

Cleric

Minister

Carl

PriestAdam Bob

Old Knowledge K:

New Knowledge N:

Cleric

Minister

Carl

PriestAdam Bob

Single Husband

John

Cleric

RentSub

Wife

Mary

hasHb

1..n

Unsatisfiable

21/31

Formula-Based Approaches

Approach: Choose a subset Kmax ⊆ K

Consistent with N Coherent with N Maximal wrt set inclusion

Result: Kmax ∪ N

Problem: In general Kmax is not unique

Cleric

Minister

Carl

PriestAdam Bob

Old Knowledge K:

New Knowledge N:

Cleric

Minister

Carl

PriestAdam Bob

Single Husband

John

Cleric

RentSub

Wife

Mary

hasHb

1..n

Single

Cleric

RentSub

Husband

John

Wife

Mary

hasHb

1..n

Satisfiable

Satisfiable

Unsatisfiable

Cleric

RentSub

21/31

What To Do? What to do with several Kmax?

Classical approaches:When In Doubt Throw It Out:

take intersection of Kmax

Cross-Product: take disjunction of Kmax

• Loses too much data• coNP-complete

Not expressible in DL-Lite

TempStaff Teaching

PhD

K ∪ NTempStaff Teaching

PhD

(Kmax2 ∩ Kmax1) ∪ N

TempStaf Teaching

PhD

TempStaf Teaching

PhD

Kmax1 ∪ N Kmax2 ∪ NOR

∨

22/31

Outline

I. Requirements for an evolution operatorII. Attempt to apply classical approaches

a) Model-Based approachesb) Formula-Based approaches

III. Our proposala) Bold Semanticsb) Careful Semantics

IV. Conclusion

Our Proposal – Bold Semantics

Take an arbitrary Kmax

Update(K, N) = Kmax ∪ N The result is non-deterministic

TempStaff Teaching

PhD

K ∪ NTempStaff Teaching

PhD

Kmax ∪ N

Can be computed in PTime23/31

How To Avoid Non-Determinism?

Preferences “reduce” non-determinism:Order over assertionsMinimality wrt cardinalityetc.

Evolution in specific cases may be deterministic:ABox evolution

24/31

ABox Evolution Is Deterministic

1. Add assertions from N2. Find conflicting assertions3. Resolve conflicts

Drawback: Mary cannot get divorced

Single Husband

Priest

Wife

John

Mary

Adam Bob

a guyJohn

Assumptions:• N is a set of ABox assertions• Evolution does not change TBox

Theorem: For a DL-Lite KB the result of ABox evolution is unique and computable in PTime.

New knowledge N: Single(John)

Woman

26/31

hasHb

1..n

1..n

(Mary, John )?Recall:

Our intuition: 2 cases1. Mary is single 2. Mary is married to another guy

Outline

I. Requirements for an evolution operatorII. Attempt to apply classical approaches

a) Model-Based approachesb) Formula-Based approaches

III. Our proposala) Bold Semanticsb) Careful Semantics

IV. Conclusion

Careful Semantics for ABox Evolution

Formula φ is unexpected for Kmax and Nif Kmax ∪ N ⊨ φ and Kmax ⊭ φ nor N ⊭ φ

In our example an unexpected formula is:φ = ∃a guy.hasHb(Mary, a guy)∧(a guy≠John)

Role-constraining formula (RCF): φ = x.R(a,x)∃ ∧(x≠c1)∧...∧(x≠cn)

Preference: We want Kmax to be careful:no unexpected RCF are allowedKmax ∪ N ⊨ φ then Kmax ⊨ φ or N ⊨ φ

Theorem: For every DL-Lite KB K and new data N, careful Kmax exists, is unique, and is computable in PTime

28/31

Careful Semantics for ABox Evolution

New knowledge N: Single(John)

1. Run bold semantics algorithm for ABox evolution

2. Find unexpected formulas φ3. Delete assertions entailing φ

Single Husband

Wife

John

Mary

a guyJohn

Unexpected formulas:φ = ∃a guy.hasHb(Mary, a guy)∧(a guy≠John)

PriestAdam Bob

WomanMary

29/31

hasHb

1..n

1..n

(Mary, John )? Recall:

Our intuition: 2 cases1. Mary is single 2. Mary is married to another guy

Outline

I. Requirements for an evolution operatorII. Attempt to apply classical approaches

a) Model-Based approachesb) Formula-Based approaches

III. Our proposala) Bold Semanticsb) Careful Semantics

IV. Conclusion

Conclusion We reviewed Model-Based Approaches to evolution

Found MBAs are inapplicable for DL-Lite evolution We reviewed classical Formula-Based Approaches

Showed hardness or inapplicability of them We proposed two novel Formula-Based Approaches

- Bold Semantics- Careful Semantics

We developed polynomial time algorithms for new semantics

31/31

Thank you!

ONTORULE ProjectONTOlogies Meets Business RULesFP 7 grant, ICT-231875http://ontorule-project.eu/

Webdam Project Foundations of Web Data Management ERC FP7 grant, agreement n. 226513http://webdam.inria.fr/

ACSI ProjectArtifact-Centric Service InteroperationFP 7 grant, agreement n. 257593http://www.acsi-project.eu/