Download - Updating ABoxes in DL-Lite
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
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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
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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
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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.
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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
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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=∅
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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}, ∅ )
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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)
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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
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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
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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
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Naïve Semantics. Algorithm
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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
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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
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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
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Future work
Combining ABox and TBox updates Implementing update algorithms Extend it to more expressive DLs
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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/
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