Updating ABoxes in DL-Lite

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

Free University of Bozen-BolzanoAMW 2010, May 2010

Outline

I. Introduction

II. Review of Model-Based Semantics

III. Formula-Based Semantics:

∙Naïve Semantics

∙Careful semantics

IV. Conclusion

Example of DL-Lite KB

Single

Lonely

SpouseMary

MarriedJohn

hasSpouse

▲

NunRachel, Patty

Concepts:

Roles:

TBox:

ABox:

MarriedSpouseSingleLonelyNun

hasSpouse

Married hasSpouse⊑ ∃∃hasSpouse Married⊑∃hasSpouse– Spouse⊑Lonely Single⊑Spouse ¬ Single⊑Spouse ¬⊑ Nun

Married(John)hasSpose(John, Mary)Nun(Rachel), Nun(Patty)

1..n

3/24

vocabulary

schema

instance

Description Logics (DLs)

DL KB consists of two parts: TBox is for structure, similar to DB schema;ABox is instance level, like DB instance

DL-Lite is a tractable fragment of OWL 2 Traditional inference tasks for static DL KBs:

(i) concept satisfiability,(ii) concept and role hierarchies,(iii) query answering

Recent interest: ontology evolution4/24

DLs for Web Services

Services: software systems supportingmachine-to-machine interoperation

Services access data through ontologies Services can be specified using ontologies To reflect changes, there are needs in:

∙ABox evolution

∙TBox evolution

5/24

Ontology Evolution

Two main types of ontology evolution:Revision and Update

Revision:∙makes KB “closer” to the real world∙the result depends on all models of

a KB Update:

∙reflects changes in the real world∙the result is modelwise

6/24

Updating DL-Lite Ontologies

We study updates for DL-Lite KBs TBox updates:

∙ TBox revision studied in [Qi,Du:2009]

∙ We studied TBox updates in [Zheleznyakov&al:2010]

ABox updates:– Initially studied in [De Giacomo&al:2006]

– This talk: we revised and extended it.

7/24

Requirements for ABox Update

Closure under updates:Update result should be expressible in DL-Lite

Efficiency:Update result should be computable in PTIME

Update should not contradict TBox Minimal change principal:

We discuss it later8/24

Outline

I. Introduction

II. Review of Model-Based Semantics

III. Formula-Based Semantics:

∙Naïve Semantics

∙Careful semantics

IV. Conclusion

Model-Based Semantics (MBS)O:

Mod(O):

Mod(U):U:

Minimaldistance

✓ ✓ ✓ ✗10/24

Single

Lonely

SpouseMary

MarriedJohn

hasSpouse

▲

NunRachel, Patty

1..n

Model-Based Semantics (MBS)

Human

Single

Unmarried Divorsed

Spouse?

O:

O’:

✓✓ ✓ ✗

Mod(O):

Mod(O’):10/24

Single

Lonely

SpouseMary

MarriedJohn

hasSpouse▲

NunRachel, Patty

1..n

Winslett's Semantics (WS)

What does minimal distance mean?This depends on semantics.

Winslett’s semantics:∙Well known∙There are works on ABox update

under Winslett’s semantics∙Representative of MBS

Distance under Winslett’s Semantics:based on symmetric difference and set inclusion

11/24

Winslett's SemanticsI:

J: K:

distance(I, J) distance(I, K)

When distance(I, J) < distance(I, K) ?AI={ John, Rachel }BI={ Mary }

AJ={ John }BJ={ Mary }

AK={ John }BK=∅

12/24

Winslett's SemanticsI:

J: K:

distance(I, J) distance(I, K)

When distance(I, J) < distance(I, K) ?AI={ John, Rachel }BI={ Mary }

AJ={ John }BJ={ Mary }

AK={ John }BK=∅

diff(I, J) = ( {Rachel}, ∅ )

12/24

Winslett's SemanticsI:

J: K:

distance(I, J) distance(I, K)

When distance(I, J) < distance(I, K) ?AI={ John, Rachel }BI={ Mary }

AJ={ John }BJ={ Mary }

AK={ John }BK=∅

diff(I, J) = ( {Rachel}, ∅ )diff(I, K) = ( {Rachel}, {Mary} )

diff(I, J) ⊂ diff(I, K)inclusion is componentwise

So, distance(I, J) < distance(I, K) iff diff(I, J) ⊂ diff(I, K)

12/24

WS: Inexpressibility in DL-Lite

Single

Lonely

Spouse

Married

hasSpouse

▲

Nun

1..n

John

Rachel Patty

MaryHaley

Single(Mary)U:

What to do with John?Intuition: two cases are most likely1. John is not married2. John is married to another girlWS: gives the third case!3. John is married to

either Rachel, or Patty,but never both

Drawback 1: WS is counterintuitive

So, O’ ⊨ Nun(Rachel) ∨ Nun(Patty)O’ ⊭ Nun(Rachel)O’ ⊭ Nun(Patty)

Drawback 2: WS is inexpressiblein DL-Lite

Mary

?

Can Mary be Lonely?

WS: NoIntuition: Why not?

The statement“Mary is Single, but not Lonely”is inexpressible in DL-Lite

Drawback 3: No complete approximation of updating under WS exists

Every MBS may have similar problems Consider Formula-Based Semantics

13/24

Outline

I. Introduction

II. Review of Model-Based Semantics

III. Formula-Based Semantics:

∙Naïve Semantics

∙Careful semantics

IV. Conclusion

Formula-Based Semantics (FBS)Married(John)Spouse(Marry)Nun(Rachel)Spouse(Marry)

Nun(Patty)

Married(John)

Nun(Patty)Single(Haley)

Married(John)Spouse(Marry)Nun(Rachel)Nun(Patty)Single(Haley)…

Single

Delighted

Spouse

Married

hasSpouse▲

Nun

1..n

ABox:

TBox:

U:

Satisfiable✓

Unsatisfiable

✗

Satisfiable✓

Single

Delighted

Spouse

Married

hasSpouse▲

Nun

1..n

FBS: closeness is measuredbetween sets of formulas

How?

In general, Omax is not unique!There are: O1

max, O2max, …

The result is: Omax ∪ U

We take a satisfiable subsetOmax ⊆ O, which is maximal wrt:

∙cardinality, or∙set inclusion, or∙some preferences

15/24

Naïve Semantics

Preference:We want an Omax such thatOmax and U are satisfiable wrt TBox

Theorem:In DL-Lite KB O there is a unique maximal subset Omax wrt set inclusion such thatOmax and U are satisfiable wrt TBox

16/24

Naïve Semantics. Algorithm

17/24

1. Add assertions from U2. Find conflicting assertions

3. Delete conflicting assertions

4. Restore assertions that may be lost in Step 3

Single

Lonely

Spouse

Married

hasSpouse

▲

Nun

1..n

John

Rachel Patty

Mary

Haley

Mary

Single(Mary), Happy(Haley)U:Possible sources of conflicts:∙Spouse ⊑ ¬ Single∙ Spouse ⊑ ¬ Nun∙Lonely ⊑ ¬ Happy

Happy

Haley

1

12

2

ABox: Lonely(Haley), Married(John),hasSpouse(John, Marry),Nun(Rachel), Nun(Patty)

Conflicts are only btw two assertions: one is implied by the old KB,another one is implied by U

Since, the result must satisfy U,we delete the assertions from the old KB

TBox, Lonley(Haley) ⊨ Single(Haley)TBox, new ABox ⊭ Single(Haley)

We lost Single(Haley)!

So, we set Single(Haley) into thenew ABox

Haley

Single(Haley), Happy(Haley), Single(Mary)

new_wife

Note thatMarried(John) ⊨ ∃hasSpouse(John)

John has divorsed, but he is stillmarried!

Drawback: Once married, John cannot divorse

Outline

I. Introduction

II. Review of Model-Based Semantics

III. Formula-Based Semantics:

∙Naïve Semantics

∙Careful semantics

IV. Conclusion

Careful subset

Role-constraining formula (RCF) has form∃x.Role(a, x)∧(x≠c1)∧…∧(x≠cn)

In our example:∃_wife.hasSpouse(John, _wife)∧(_wife≠Mary)

Subset A’ of ABox is careful wrt U ifffor every RCF φif A’ ∪ U ⊨ φ then A’ ⊨ φ or U ⊨ φ

If it does not hold,we say that φ is unexpected

19/24

Careful Semantics

Preference:We want an Omax such thatOmax and U are satisfiable wrt TBox andOmax is careful wrt U

Theorem:In DL-Lite KB O there is a unique maximal subset Omax wrt set inclusion such thatOmax and U are satisfiable wrt TBox andOmax is careful wrt U

20/24

Careful Semantics. Algorithm

212/4

1. Run Naïve Semantics Algorithm

2. Find unexpected formulas φ’s3. Delete assertions entailing φ’s

Single

Lonely

Spouse

Married

hasSpouse

▲

Nun

1..n

John

Rachel Patty

Mary

Haley

Mary

Happy

Haley

Haley

_wife

ABox: Lonely(Haley), Married(John),hasSpouse(John, Marry),Nun(Rachel), Nun(Patty)

NaïveHappy(Haley), Single(Mary)Single(Haley),

Unexpected φ: ∃_wife.hasSpouse(John, _wife) ∧(_wife≠Mary)

Old ABox ⊭ φ, Mary was John’s wifeU ⊭ φ, it is easy to check

Single(Mary), Happy(Haley)U:

φ is entailed by:∙ Married(John) is from old ABox∙ Single(Mary) is from U

new

Outline

I. Introduction

II. Review of Model-Based Semantics

III. Formula-Based Semantics:

∙Naïve Semantics

∙Careful semantics

IV. Conclusion

Conclusion

MBS have drawbacks forDL-Lite TBox updates

We proposed Naïve semantics We proposed Careful semantics We developed a polynomial time

algorithms to compute update under both of the semantics

23/24

Future work

Combining ABox and TBox updates Implementing update algorithms Extend it to more expressive DLs

24/24

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/

References

[De Giacomo&al:2006] On the update of description logic ontologies at the instance level.

In: Proc. of the 21st Nat. Conf.on Artificial Intelligence (AAAI 2006).1271–1276

[Zheleznyakov&al:2010] Updating TBoxes in DL-Lite.In: Proc. of the 23rd International

Workshop on Description Logics(DL 2010)

[Qi,Du:2009] Model-based revision operators for terminologies in description logics.

In: Proc. of the 21st Int. Joint Conf.on Artificial Intelligence (IJCAI 2009).891–897