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### Ontology EvolutionUnder Semantic Constraints

Outline

Bernardo Cuenca Grau, Ernesto Jiménez-RuizComputer Science Department, University of Oxford

Evgeny Kharlamov, DmitriyZheleznyakovKRDB research centre, Free University of Bozen-Bolzano

KR 2012, Rome

Ontologies: schema + data

- Schema provide
- standard vocabularies for data
- classes (concepts)
- properties (roles)
- a way to structure data
- means for machines to be able to understand data
- Data is a collections of facts
- Instantiations of classes
- Instantiations of properties

Domain Ontologies

- Goal: to provide standard vocabularies to communities
- Clinical sciencesontologies:
- SNOMED CT: Systematized Nomenclature of Medicine - Clinical Terms
- > 311k concepts
- NCIt: National CancerInstitute thesaurus
- ~ 89k concepts, 200m cross links between them [NCI]
- FMA: Foundational Model of Anatomy
- 75k classes, 168k relations, 120k terms, 3.1m relat. inst.

Evolution of Domain Ontologies

- Evolution of SNOMED:
- 5 geographically distributed teams making modifications
- every 2 weeks the main team integrates changes, resolves conflicts
- from 2002 to 2008 SNOMED went from 278k to 311k concepts [SM-1]
- Evolution of NCIt:
- 20 full time editors for NCI
- Developers of NCI do over 900 monthly changes [HKR’08]
- Evolution of FMA:
- FMA “is an evolving computer-based knowledge source ...” [FMA]

Evolution of Domain Ontologies

- At the high level ontologies are changed by
- addition of information
- usually referred as revision or update
- deletion of information
- usually referred as contraction
- Evolution may affect both
- schema level
- data level
- A natural requirement: principle of minimal change;

changes should minimally affect ontology

- structure
- semantics

Languages for Domain Ontologies

- Evolution of ontologies is a classical problem in KR
- intensively studied for propositional logic
- there are different semantics for evolution
- many complexity results
- very few results beyond “propositional paradise”
- Ontology Web Language: OWL 2 – W3C standard
- OWL 2 (based on SROIQ)
- OWL 2 QL (based on DL-Lite)
- OWL 2 EL (based on EL, EL++)
- e.g. SNOMED

these are not propositional

Outline

- Existing approaches to evolution
- Syntactic approach
- Deductive approach
- Our approach: evolution under constraints
- Conclusion & directions

SA: Evolution Process

- add/delete
- minimal change(syntactic)

processing

- ontologyin L

- evolvedontologyin L

- operator

- newinfo

either axioms to add

or axioms to delete

E.g., contraction operator: takes a maximal subset (w.r.t. set inclusion) of the original ontology which does not entail axioms to be deleted

Syntactic Approach to Evolution

- In the ontology:
- “Oenophiles are gourmets”
- “Oenophiles are not koalas”
- To delete: “Oenophiles are gourmets”
- To this end it is enough to delete

[HS’05]

[KPSCG’06]

[JRGHB’11]

and

- In the resulted ontology:
- “Oenophiles are not gourmets”
- “Oenophiles are not koalas” is lost

OK

Not desirable

Outline

- Existing approaches to evolution
- Syntactic approach
- Deductive approach
- Our approach: evolution under constraints
- Conclusion & directions

DA: Evolution Process

- add/delete
- minimal change

represent

expand

processing

processing

- evolvedclosurein L

- ontologyin L

- closurein L

- evolvedontologyin L

- operator

- newinfo

either axioms to add

or axioms to delete

E.g., contraction operator: takes a maximal subset (w.r.t. set inclusion)of the ontology deductive closure which does not entail axioms to be deleted

What Is Known?

- DA have been studied for propositional logic
- WIDTIO
- Cross-product
- …
- What about ontologies?
- Practical extensions of SA to preserve certain inference
- [JRGHB’11] implemented in ContentCVS
- “Manchester” grammar [GPS’12]: extension of [JRGHB’11]with combination of sub-concepts of the ontology

axiom A ⊑ B | A ⊑ ¬ B | A ⊑ ∃ R.B | A ⊑ ∀ R.B

Syntactic Approach to Evolution

- In the resulted ontology:
- “Oenophiles are not gourmets”
- “Oenophiles are not koalas” is lost
- ContentCVS & “Manchester” grammar allow to restore the missing disjointness

OK

Not desirable

Outline

- Existing approaches to evolution
- Syntactic approach
- Deductive approach
- Our approach: evolution under constraints
- Conclusion & directions

Our Proposal in a Nutshell

- Generalization of SA and DA under a common framework
- Our view of principle of minimal change
- maximize preservation of ontology structure
- maximize preservation of ontology entailments
- Preservation language (LP) tells us which class of entailments should be maximized
- ContentCVS & “Manchester grammar” are instantiations for particular “finite” LP

Evolution Process

- add/delete
- minimal change

represent

expand

processing

- sub-ontologyin L

- sub-ontologyin LO

- evolvedclosurein LP

- evolvedclosurein L

- ontologyin LI

- closurein LP

- ontologyin L

- closurein L

- evolvedontologyin L

- evolvedontologyin LO

- operator

- newinfo

either axioms to add

or axioms to delete

Evolution under Semantic Constraints

processing

- sub-ontologyin LO

- ontologyin LI

- closurein LP

- operator

- evolvedontologyin LO

- evolvedclosurein LP

- semanticconstraints
- (C+,C-)

- C+: axioms that should be present in the result
- C−: axioms that should be absent in the result

- General evolution encompasses both
- contraction via C−
- revision via C+

Example: Contraction

processing

- sub-ontologyin LI

- Task: delete an axiom A1 ⊑ A2 from an LI-ontology K
- LO-ontology K’is a contraction of an LI-ontology Kw.r.t. A1 ⊑ A2 if:
- K’⊭ A1 ⊑ A2
- K⊨ K’
- Contraction may not be optimal

- ontologyin LI

- closurein LP

- operator

- evolvedontologyin LO

- evolvedclosurein LP

- semanticconstraints
- (∅,C-)

LI: input lang.

LO: output lang.

LP: preservation lang.

Example: Contraction

processing

- sub-ontologyin LI

- ontologyin LI

- closurein LP

- operator

- evolvedontologyin LO

- evolvedclosurein LP

- semanticconstraints
- (∅,C-)

- newdta

LI: input lang.

LO: output lang.

LP: preservation lang.

- Task: delete an axiom A1 ⊑ A2 from and LI-ontology K
- AcontractionK’ of K isoptimalw.r.t. LP if it maximally preserves:
- structure of KK’ ∩ K⊄ K’’∩ Kfor every contr. K’’
- LP-entailments of Knot true: if K’⊨α then K’’⊨α for every contr. K’’

Evolution with Finite LP

processing

- sub-ontologyin LO

- Ontology language Lover a finite signatureΣisfinite if there are finitely many non-equivalent L-formulas over Σ
- Examples of LP:
- ContentCVS &”Manchester” grammars finite
- OWL 2 QL (DL-Lite) finite
- OWL 2 EL (EL, EL++, FL0) infinite

- ontologyin LI

- closurein LP

- operator

- evolvedontologyin LO

- evolvedclosurein LP

- semanticconstraints
- (C+,C–)

Evolution with Finite LP

processing

- sub-ontologyin LO

- ontologyin LI

- closurein LP

- operator

- evolvedontologyin LO

- evolvedclosurein LP

- semanticconstraints
- (C+,C–)

always exists

finite LP

Theorem: If the preservation language LP is finite, then

- an optimal evolution always exists (provided an evolution exists)
- both O and LP-closure of O are finite we can simply write the result

Evolution with Infinite LP

processing

- sub-ontologyin LO

- ontologyin LI

- closurein LP

- operator

- evolvedontologyin LO

- evolvedclosurein LP

- semanticconstraints
- (C+,C–)

finite representationmay not exist

infinite LP

- What if LP is infinite?
- We have a problem!
- Optimal evolution may not exist!

Evolution with Infinite LP

processing

- sub-ontologyin LO

- ontologyin LI

- closurein LP

- operator

- evolvedontologyin LO

- evolvedclosurein LP

- semanticconstraints
- (C+,C–)

FL0

EL

FL0

EL

EL

FL0

Theorem:

- If FL0 setting optimal evolution does not exist in general
- If EL setting optimal evolution does not exist in general
- complex interaction of cycles and recursions

Infinite LP: Exponential Case

processing

- sub-ontologyin LO

- ontologyin LI

- closurein LP

- operator

- evolvedontologyin LO

- evolvedclosurein LP

- semanticconstraints
- (∅,C-)

acyclic EL

acyclic EL

chain EL

cyclic

- ChainEL consists of inclusion assertions
- A1⊑ ∃R1…Rn.A2or
- ∃R1…Rn.A1 ⊑ A2
- It is a simple infinite language to study expressibility

- An acyclic ontology has acyclic canonical model
- SNOMED and NCItare acyclic

- opt. contraction always exists
- EXP time computation

Infinite LP: Polynomial Case

processing

- sub-ontologyin LO

- ontologyin LI

- closurein LP

- operator

- evolvedontologyin LO

- evolvedclosurein LP

- semanticconstraints
- (∅,C-)

non-rec EL

non-rec EL

chain EL

non-recursive

- An ontology is non-recursiveif concepts of the form ∃R.C donot appear at the left-hand side of axioms
- Simplest non-recursive EL sub-language

- opt. contraction always exists
- PTimecomputation

Summary

ruled out by LP

- Existing approaches to evolution
- Syntactic approach
- Deductive approach
- Our approach: evolution under constraints
- Conclusion & directions

Conclusion & Directions

- We introduced SDA:
- a novel framework for ontology evolution
- SDA generalizes:
- syntactic approaches and
- deductive approaches
- it provides flexible means to navigate between SA and DA

We studied 4 settings for SDA:

- Directions:
- extend the current results to richer LP: chain EL ?
- evolution beyond EL

References

- [HKR’08] Hartung, M.; Kirsten, T.; and Rahm, E. 2008. Analyzing the evolution of life science ontologies and mappings. In Proc. of DILS, 11–27.
- [SM-1] http://www.ihtsdo.org/snomed-ct/snomed-ct0/adoption-of-snomed-ct/
- [FMA] http://sig.biostr.washington.edu/projects/fm/AboutFM.html
- [NCI] https://wiki.nci.nih.gov/display/EVS/NCI+Thesaurus+versus+NCI+Metathesaurus
- [HS’05]Haase, P., Stojanovic, L.: Consistent evolution of OWL ontologies. In: ESWC. (2005)
- [KPSCG’06] Kalyanpur, A., Parsia, B., Sirin, E., Grau, B.C.: Repairingunsatisfiableconcepts in OWL ontologies. In: ESWC. (2006) 170–184
- [JRCGHB’11] Jimenez-Ruiz, E., Cuenca Grau, B., Horrocks, I., Berlanga, R.: Supporting concurrent ontology development: Framework, algorithms and tool. DKE. 70:1 (2011)
- [GPS’12]: Rafael S. Gonçalves, BijanParsia, Ulrike Sattler. 2012. Concept-based semantic difference in expressive description logics. In Proc. of DL

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