Applying Belief Change to Ontology Evolution

PhD StudentComputer Science Department

University of Cretefgeo@csd.uoc.gr

Giorgos Flouris

Research AssistantInstitute of Computer Science

FORTHfgeo@ics.forth.gr

PhD Thesis Summary

ISWDS 0507/11/05

Part Overview

(“Elevator Talk”)

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

Summary of Results

Logics (under Tarski’s model)

AGM-compliantlogics

AGM Class

Base-AGM-compliantlogics

DLs(OVA)

DLs(CVA)

OWL

DLs

Part Research Description

Ontology Evolution:Definition 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– …

Output Ontology

Ontology Evolution Input Ontology

Success

Fail

Change Representation Semantics of Change

Implementation Change Propagation

Validation

Change Capturing “penguins can’t fly”

Add_IsA(…)

Penguin⊑Fly

User: , , ,

System: ,

Current Approaches

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

Proposed Approach

User:

System: , , , ,

Output Ontology

Ontology Evolution Input Ontology

Success

Fail

Change Representation Semantics of Change

Implementation Change Propagation

Validation

Change Capturing “penguins can’t fly”

Add_IsA(…)

Penguin⊑Fly

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

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

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

A More Specific Approach:the 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

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

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 Tarski’s 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)

Results(AGM-Compliance)

Logics (under Tarski’s model)

AGM-compliantlogics

AGM Class

Further Results

• Connection with lattice theory:– Every logic can be described by a lattice– AGM-compliance can be determined by the lattice’s

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)

Results(Base-AGM-Compliance)

Logics (under Tarski’s model)

AGM-compliantlogics

AGM Class

Base-AGM-compliantlogics

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, owl:imports): all non-AGM-compliant

Results(AGM-Compliance and DLs)

Logics (under Tarski’s model)

AGM-compliantlogics

AGM Class

Base-AGM-compliantlogics

DLs(OVA)

DLs(CVA)

OWL

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

………

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

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