D. Calvanese, E. Kharlamov, W. Nutt, and D. Zheleznyakov KRDB Research Centre Free University of...

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

KRDB Research CentreFree University of Bozen-Bolzano

FBK, January 2011

Understanding Evolution of Semantically Annotated Data

World Wide Web and Evolution Web content is ubiquitously dynamic (Textual) Web content has two flavors:

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Plain (HTML) data~ semantics understandable by people

Semantically annotated data (knowledge) ~ semantics understandable by machines

We focus on the second kind of data which is believed to be the Web of tomorrow [TBL99]

Our goal:To understand how to incorporate the new knowledge into the old one~ to study evolution of knowledge

date namelang.

Semantic Annotations

Ontologies are a prime mechanism to bring semantics to the Web, they provideannotations (e.g., date, name)meta annotations (e.g., class, property)classifications of annotations (e.g., subclass-of)properties of annotations (e.g., domain, range)…

Technologies behind ontologiesResource description Framework (RDF)Ontology Web Language (OWL)Rule Languages (e.g. OWL 2 RL)

We focus on OWL 2, its one profile: OWL 2 QLwhich is based on a Description Logics family: DL-Lite

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Description Logics (DLs)

Cleric

Priest

Husband

Concepts are classes of objects

Roles are relations between objects

ABox isfor instances of concepts and roles

TBox is for structure of the knowledge

Carl

JohnAdam

Bob

DL Ontology (Knowledge Base):

TBox:

ABox:

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Example of a Knowledge Base

Single Husband

Priest

Wife

hasHb

Concepts:

Roles:

TBox:

ABox:

Wife, Husband, Single, Woman, Priest

HasHb

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

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DL-Lite Language

TBox assertions: Formulas of the form:inclusion: disjointness:functionality:

ABox assertions: instanciations: concept:role:

No disjunction and no negation on the left of inclusions

DL-Lite ~ a bit extended Horn Logic with existential variables in head

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A R, A R⊑ ∃ ⊑ ∃ − , A B, ...⊑

(func R), ...A ¬ R, A ¬B, ...⊑ ∃ ⊑

B(a), R(a), ...∃

R(a,b), ...

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

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Is Evolution Solved for DLs?

Traditional inference tasks for DL KBs are static: concept satisfiabilityKB satisfiabilityconcept and role hierarchiesquery answering

Research on ontology evolution is quite youngABoxes in expressive DLs:

Liu, Lutz, Milicic, and Wolter ABoxes in DL-Lite:

De Giacomo, Lenzerini, Poggi, RosatiTBoxes in DLs and DL-Lite: Qi, Du…

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[Qi,Du’09]

[Giacomo&al’06]

[Liu&al‘06]

Outline

I. The problem of evolution

II. Formalizing evolution

III. Attempt to apply classical approachesa) Model-Based approachesb) Formula-Based approaches

IV. Our proposala) Bold Semanticsb) Careful Semantics

V. 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 KB

Evolved 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⊑

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Technical Requirements

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

Efficiency:Evolution result should be computable in PTime

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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

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Are these approaches applicable to DL-Lite evolution?

Outline





V. 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)

Take some models of Mod(N) (since new knowledge should be preserved)

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

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

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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

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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’:

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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

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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’:

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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 ⊖ J

dist|⊖| (I,J) = |I ⊖ J|

dist⊖(I,J) = {q, r, s}

dist|⊖| (I,J) = 3

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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

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What is distance



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}

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What is distance



global: G

local: L

symbols: S

atoms: A

Two possibilities for each of three dimensions

⇒ eight possible semantics

Theorem (Inexpressibility):

For all of eight semantics the result of the evolutioncannot be expressed in DL-Lite

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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 cases

1. 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

Woman

Mary

1..n

(Mary, John )?

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Observation: In [Giacomo&al’06]

• evolution of ABoxes in DL-Lite • fixed TBoxes• under global semantics on atoms • algorithm to compute semantics is provided

⇒ Their results are wrong

What Else May Go Wrong?Single Husband

Priest

Wife

hasHb

1..n

MBAs give a strange models M:M = { Bishop(Carl), Priest(Carl), ¬Single(Carl), … }Thus, KB’ Priest Single⊭ ⊑

John

Adam Bob

New Knowledge: Bishop Priest⊑

How does it affect the old KB?

Our intuition:

Just add the new assertion to the old KB

Woman

Mary

1..n

(Mary, John )

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Bishop

Carl

Drawback 1: it is counterintuitiveDrawback 2: inexpressible in DL-Lite

Observation: In [Qi,Du’09]

• evolution of TBoxes • in KBs with empty ABoxes • under global semantics on atoms

⇒ Their operator does not work

for general KBs in DL-Lite

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

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Outline





V. 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

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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

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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

∨

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Outline





V. Conclusion

Our Proposal – Bold Semantics

Take an arbitrary Kmax

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

TempStaff Teaching

PhD

K ∪ NTempStaff Teaching

PhD

Kmax ∪ N

Can be computed in PTime

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How To Avoid Non-Determinism?

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

Evolution in specific cases may be deterministic:ABox evolution

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ABox Evolution Is Deterministic

1. Add assertions from N

2. Find conflicting assertions

3. 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

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hasHb

1..n

1..n

(Mary, John )?

Recall:

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

Outline





V. Conclusion

Careful Semantics for ABox Evolution

Formula φ is unexpected for Kmax and N

if 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

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Careful Semantics for ABox Evolution

New knowledge N: Single(John)

1. Run bold semantics algorithm for ABox evolution

2. Find unexpected formulas φ

3. Delete assertions entailing φ

Single Husband

Wife

John

Mary

a guyJohn

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

Priest

Adam Bob

Woman

Mary

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hasHb

1..n

1..n

(Mary, John )? Recall:

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

Outline





V. 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

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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/

References

[TBL’99] - M. Fischetti, T. Berners-Lee. Weaving the Web. HarperSanFrancisco, 1999.

[Liu&al’06] - H. Liu, C. Lutz, M. Milicic, and F. Wolter. Updating Description Logic ABoxes. KR06.

[Giacomo&al’06] - G. De Giacomo, M. Lenzerini, A. Poggi, R. Rosati: On the Update of Description Logic Ontologies at the Instance Level. AAAI 2006

[Qi,Du’09] - G. Qi, J. Du: Model-based Revision Operators for Terminologies in Description Logics. IJCAI 2009

D. Calvanese, E. Kharlamov, W. Nutt, and D. Zheleznyakov KRDB Research Centre Free University of...

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