Methods for Resolving Inconsistent Ontologies

1
Methods for Resolving Inconsistent Ontologies
Joey Lam 24 July 2006
2
Overview

• Introduction
• OWL Ontology
• Existing Approaches
• Proposed Approach
• Confidence of Axioms
• Rewriting Axioms
• Empirical Study
• Evaluation
• Deliverables and Work plan

3
Introduction

• Ontology languages become more expressive
• Resolving inconsistencies in ontologies is a
  challenging task for ontology modelers.
• Standard Description Logic (DL) reasoning
  services can check if an ontology is consistent
  however, no support for resolving
  inconsistencies.

4
Introduction

• Ontology languages become more expressive
• Resolving inconsistencies in ontologies is a
  challenging task for ontology modelers.
• Standard Description Logic (DL) reasoning
  services can check if an ontology is consistent
  however, no support for resolving
  inconsistencies.
• Research Question
• How can we improve the process of resolving
  inconsistent ontologies in an ontology management
  environment?

5
OWL Ontology

• An OWL ontology is a set of axioms
• Class Axioms C ? D, C D
• Role Axioms R ? S, Func(R), Trans(S)
• Individual Axioms aC, lta,bgtR

6
Unsatisfiable Class

• Unsatisfiable classes are those which cannot have
  any possible individual, i.e. CI ? for all
  models I of the ontology

7
Inconsistent Ontology

• An ontology is inconsistent iff it has no models

• Inconsistent ontologies are those which have a
  contradiction in the individual data. e.g. an
  individual of an unsatisfiable class

8
Existing Approaches (1)

• Pinpoint the so called Minimal Unsatisfiability
  Preserving Sub-ontologies (MUPSs), which are sets
  of axioms responsible for an unsatisfiable
  concept
• Reference S. Schlobach and R. Cornet. 2003

9
Existing Approaches (2)

• Calculate Maximally Concept-Satisfiable
  Sub-ontologies (MCSSs), MCSSs are obtained by
  removing just enough axioms to eliminate all
  errors.
• Reference T. Meyer, K. Lee, R. Booth, and J. Z.
  Pan. Finding maximally satisfiable terminologies
  for the description logic ALC, 2006

10
Existing Approaches (2)
(i) Bird ? Animal ? CanFly (ii) Penguin ? Bird ?
?CanFly (iii) Eagle ? Bird
MCSS (i) Bird ? Animal ? CanFly (iii) Eagle ?
Bird Or (ii) Penguin ? Bird ? ?CanFly (iii) Eagle
? Bird
11
Limitation of Existing Approaches

• Leave it up to the user to modify the errors
  or provide the user with a set of maximal
  coherent ontologies.
• No further support for selecting which
  problematic axioms to remove or modify
• No support for rewriting axioms

12
What is needed are

• methods to rank potentially problematic axioms to
  give the user guidance on which ones should be
  removed or modified
• methods to rewrite the problematic axioms.

13
Proposed Approach

• Extend the existing approach to finding Maximal
  Concept-Satisfiable Sub-ontologies (MCSSs)
• Rank the problematic axioms based on their
  confidence values
• Structural Heuristics
• Historical usage heuristics
• Rewrite the axioms which are excluded from MCSSs,
  rather than to directly remove them from the
  ontology.
• harmful changes
• helpful changes

14
Confidence Value

• The confidence value indicates how confident we
  are of the correctness of the axioms in an
  ontology we want to exclude the axioms with the
  least confidence and preserve the ones with the
  highest confidence.
• confidence a ? -1, 1

15
Confidence values of Axioms Structural
Heuristics

• Syntactic Relevance Measurement
• Two concepts which are connected by a long chain
  of axioms are less relevant than those connected
  by a short chain

• Similarity between Sibling Classes
• Sibling classes usually participate in similar
  relationships, but are disjoint with each other
• If we know Student and Staff are siblings,
  then the confidence of a3 Student ??Staff should
  be higher.

16
Confidence values of Axioms Historical usage
heuristics

• Case 1 the information is reliable
• newly added axioms (or recently modified) are
  usually more accurate gt higher confidence.
• Case 2 the information is unreliable
• newly added axioms gt lower confidenceolder
  axioms gt higher confidence
• Case 3 the reliability is unknown
• The confidence of an axiom is inversely
  proportional to the frequency of its
  modifications.

17
Aggregating Confidence Values

• confidence(a) wpathconfidencepath(a)
  wsibconfidencesib(a) wdisj confidencedisj(a)
  wusageconfidenceusage(a)

• The MCSS with the lowest confidence for its
  excluded axioms is recommended

18
Strategies for Rewriting Axioms

• Improperly rewriting a problematic axiom may not
  resolve the unsatisfiability, and could introduce
  additional unsatisfiability

• Harmful Change
• replace a concept in an axiom, but this
  replacement will still keep the unsatisfiability,
  or invoke additional unsatisfiabilities
• Helpful Change
• replace a concept in an axiom, this replacement
  is not a harmful change, will resolve the
  unsatisfiability, and compensate for the lost
  entailments.

19
Helpful and Harmful Change

• Revise the tableau-base algorithm to trace which
  parts of the axioms are responsible for the
  unsatisfiability
• Reference F. Baader and B. Hollunder. Embedding
  defaults into terminological knowledge
  representation formalisms. J. Autom. Reasoning,
  14(1)149-180, 1995.
• T. Meyer, K. Lee, R. Booth, and J. Z. Pan.
  Finding maximally satisfiable terminologies for
  the description logic ALC. In Proceedings of the
  21st National Conference on Artificial
  Intelligence (AAAI-06), July 2006.

(i) Bird ? Animal ? CanFly (ii) Penguin ?
Bird ? ?CanFly (iii) Eagle ? Bird
20
Helpful and Harmful Change

• (i) Bird ? Animal ? CanFly
• (ii) Penguin ? Bird ? ?CanFly
• (iii) Eagle ? Bird
• Harmful changes to replace CanFly in (i) are ?
  Animal, Penguin, and Eagle
• Helpful change to replace Bird in (ii) is Animal

21
Empirical Work

• Identify the heuristics used by knowledge
  engineers when facing inconsistencies in
  ontologies
• Investigate how they resolve the unsatisfiable
  concepts in ontologies
• Focus on how they explore their ontology
  knowledge and cope with the unsatisfiabilities

22
Types of Ontological Inconsistency

• Complement (A ? C ? ?C)
• A complementary inconsistency occurs when an
  instance belongs to a class and its complement
• Disjointness (A ? C ? D, C ? ?D)
• A disjointness inconsistency occurs when an
  instance belongs to two or more classes which are
  disjoint
• Cardinality (A ? n.R, A ? m.R, m n)
• A cardinality inconsistency occurs when an
  instance has a maximum (minimum) cardinality
  restriction but is related to more (fewer)
  distinct individuals
• Datatype
• A literal value violates the (global or local)
  range restrictions on a datatype property

23
Task Types

• Ontologies with one inconsistency and concrete
  concepts
• Ontologies with one inconsistency and abstract
  concepts
• Ontologies with multiple inconsistencies and
  concrete concepts
• Ontologies with multiple inconsistencies and
  abstract concepts

24
Presentational Styles

• a list of problematic axioms,
• associated natural language explanations
• graphical representations
• Staff ? ?Student
• Staff are not students
• Part-time Staff ? Staff
• Part-time staff are staff
• Research Student ? Student
• Research students are students
• PhDStudent ? Part-time Student
• PhD Students are part-time students

25
Detailed Planning

• Procedure
• Pilot experiments are run with subjects who are
  (not) familiar with DLs
• Subjects have to rate which presentational form
  is most helpful/supportive
• The subjects verbal explanations will be taped
  and all notes retained

26
Evaluation

• Performance Evaluation
• Evaluation with real-world ontologies
• Benchmarking with existing test-sets
• Usability Evaluation
• Usability-study with 2 groups of subjects
• Time taken by subjects for debugging ontologies
• Acceptance of axiom ranking and suggested
  rewriting of axioms

27
Deliverables

• Submitted Papers
• ISWC 2006
• WI 2006
• Technical Report on the empirical study
• An ontology management tool for debugging
  ontologies
• Thesis

28
Work Plan

• Work done so far
• Two Submitted Papers
• Implemented MCSS
• Pilot Experiment
• Future Work
• Empirical Study
• Optimisation of algorithms
• Evaluation
• Plug-in for Protégé
• Thesis write-up

29

• Questions?