Applying Belief Change to Ontology Evolution

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Applying Belief Change to Ontology Evolution
Giorgos Flouris
PhD Thesis Summary

• PhD StudentComputer Science DepartmentUniversity
  of Cretefgeo_at_csd.uoc.gr

Research AssistantInstitute of Computer
ScienceFORTHfgeo_at_ics.forth.gr
ISWDS 0507/11/05
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Part ?Overview(Elevator Talk)
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Ontology Evolution and Belief Change

• We propose a different viewpoint on ontology
  evolution
• Addressing the problem of ontology evolution
  using techniques from belief change
• In particular
• AGM theory of contraction
• In ontologies represented using some DL or OWL
  flavor

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Summary of Results
DLs(CVA)
Base-AGM-compliantlogics
OWL
DLs(OVA)
DLs
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Part ?? Research Description
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Ontology EvolutionDefinition and Importance

• Ontology evolution is the process of modifying an
  ontology in response to a certain change in the
  domain or its conceptualization
• Main reasons for ontology evolution
• Dynamic domains
• Change in users needs or perspective
• New information (previously unknown, classified
  or unavailable) that improves the
  conceptualization
• Errors during original conceptualization
• Ontology dependency

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Ontology Evolution
Change Capturing ? penguins cant fly
Penguin??Fly
Change Representation ?Semantics of Change ?
Add_IsA()
Implementation ?Change Propagation ?
Success
Validation ?
Fail
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Limitations

• Main limitations of current approaches
• Manual or semi-automatic approaches
• Too many operators (complex and atomic)
• No formal semantics
• Cause problems
• Automated agents and systems
• Scalability
• Formal properties unknown
• Bottleneck for current research

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Ontology Evolution
Change Capturing ? penguins cant fly
Penguin??Fly
Change Representation ?Semantics of Change ?
Add_IsA()
Implementation ?Change Propagation ?
Success
Validation ?
Fail
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Why Belief Change?(1/2)

• Knowledge should be up-to-date
• Keeping KBs up-to-date belief change
• Keeping ontologies up-to-date ontology evolution
• Ontology evolution can be viewed as a special
  case of belief change
• View belief change techniques, ideas, intuitions,
  results, algorithms and methods under the prism
  of ontology evolution
• We address ontology evolution using belief change

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Why Belief Change?(2/2)

• Belief change properties
• Mature
• Formal
• Automatic
• Addresses important issues that have not been
  considered in ontology evolution
• Revision and Update
• Revision and Contraction
• Postulations vs Explicit Constructions
• Foundational vs Coherence Theories
• Principle of Minimal Change
• Principle of Primacy of New Information

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Difficulties and Methodology

• Belief change techniques are generally targeted
  at classical logic
• Their assumptions fail for DLs and other
  ontological languages
• Cannot be directly used for such logics
• But the underlying intuitions are applicable
• Belief change techniques need to be migrated to
  the ontology evolution context
• PhD, Phase 1
• Set the foundations for future work on the
  subject
• Very abstract, long-term and ambitious goal

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A More Specific Approachthe AGM Theory

• For the purposes of this PhD, we restricted
  ourselves to deal with
• The most influential belief change theory (AGM
  theory)
• The most fundamental operation (contraction)
• The most promising languages for ontological
  representation (DLs and OWL)
• PhD, Phase 2
• Study the applicability of the AGM theory of
  contraction in DLs and OWL

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AGM Theory

• AGM theory (Alchourron, Gärdenfors, Makinson)
• The most influential approach in belief change
• Contraction
• The most fundamental operation for theoretical
  purposes
• Deals with the removal of knowledge from a KB
• Main contribution 6 AGM postulates that
  determine whether a contraction operator behaves
  rationally
• AGM theory is based on certain assumptions on the
  underlying logic, so, as usual
• Intuitions applicable in ontologies
• Postulates and results not applicable in
  ontologies

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AGM-Compliance

• Dropped the AGM assumptions and considered the
  class of logics studied by Tarski
• Very general class of logics (that contains DLs)
• We generalized the AGM theory (and postulates) to
  be applicable to Tarskis class
• Noticed that only some of the logics in this
  class admit an operator satisfying the
  generalized postulates (i.e., a rational
  operator)
• Termed AGM-compliant logics (3 characterizations)

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Results(AGM-Compliance)
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Further Results

• Connection with lattice theory
• Every logic can be described by a lattice
• AGM-compliance can be determined by the lattices
  structure
• Connection with the foundational model
• AGM theory based on the coherence model
• There are logics in which a foundational AGM
  theory can be applied
• Termed base-AGM-compliant logics (2
  characterizations)

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Results(Base-AGM-Compliance)
Base-AGM-compliantlogics
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AGM-Compliance and DLs

• Studied DLs (two types)
• CVA (Closed Vocabulary Assumption) allows the
  description of the ontological signature using DL
  axioms
• OVA (Open Vocabulary Assumption) ignores the
  signature because it cannot be described using DL
  axioms
• DLs (CVA) non-AGM-compliant
• DLs (OVA) some are AGM-compliant, some are not
• Introduced results, heuristics, rules of thumb
• OWL (different flavors, CVA or OVA, annotation
  features, owlimports) all non-AGM-compliant

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Results(AGM-Compliance and DLs)
DLs(CVA)
Base-AGM-compliantlogics
OWL
DLs(OVA)
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Partial List of DLs (OVA)
AGM-compliant DLs Non-AGM-compliant DLs
? ALCO?,? ? ALC?,? with no Abox ? ALCO with no axioms involving role terms ? ALC with empty Abox and no axioms involving role terms ? All DLs with more operators (but no more connectives) than the above DLs ? SH, SHI, SHIN, SHOIN, SHOIN(D), SHOIN, SHOIN(D), SHIQ, SHIF, SHIF(D), SHIF, SHIF(D) ? FL0, FL? with role axioms ? All DLs between ALH and ALHCIOQ ? OWL DL, OWL Lite without annotations and all flavors of OWL with annotations
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Conclusion

• Phase 1
• Proposed the study of ontology evolution from a
  different perspective, using belief change ideas
  and terminology
• Phase 2
• Focused on the AGM theory of contraction
• Determined its applicability to DLs and OWL

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Future Work

• Study other belief change approaches
• Connection of AGM-compliance with other
  AGM-related results
• The operation of revision
• Levi identity
• Representation theorems
• The development and/or implementation of a
  specific algorithm for integration into ontology
  evolution tools