Inferring with Ontologies

1
Inferring with Ontologies

• Atilla ELÇI
• Dept. of Computer Engineering
• Eastern Mediterranean University

2
TerminologyThe Role of Philosophy in SemWeb

• A point of view by Christopher Menzelof Texas
  AM University
• Formal Ontology and Philosophical Content on
  the Semantic Web,APA Symposium on Formal
  Ontologyand Philosophical Content on the
  Semantic Web, San Francisco, 28 March 2003Note
  Contributions to Automated Reasoning Systems
  in the text, (local copy).
• Philosophers point of view Logic Ontology by
  Thomas Hofweber. 2004. Entry in Stanford
  Encyclopedia of Philosophy.

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TerminologyLogic Inference

• Descriptive Logic versus Rule-based dilemma
• RuleML approach Ch.5 in A Semantic Web Primer by
  Grigoris Antoniu Frank van Harmelen, The MIT
  Press, 2004. pp 151-178.
• Basic terms L/FOL/SOL reference the short intro
  in Passin Section 6.2- All logics arent created
  equal
• Inference article in Wikipedia as a round
  introduction of the term.

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TerminologyInference, aka Reasoning

• Inference article in Wikipedia as a round
  introduction of the term.
• An example the classic syllogism
• Automatic logical inference
• Inference and uncertainty Nonmonotonic Reasoning
• "Evaluating Reasoning Systems Ontology Languages
  " Ontolog Mini Series by Professor Michael
  Gruninger study slides
• 3 Ontology spectrum
• 19-21 Description logics

5
Expressivity of reasoning languages

• Section 3 Reasoning in Evaluating Reasoning
  Systems, NISTIR 7310 Deliverable, May 2006
• 3.1 Introduction to Reasoning
• 3.2 Representation Languages
• 3.2.1 First-Order Logic define.
• 3.2.3.4 Second-Order Logic
• 3.2.4 Reified First-Order Logics
• 3.2.5 Description Logics
• 3.2.6 Web Languages
• 3.2.6.1 RDF/S
• 3.2.6.2 OWL
• 3.2.8 Nonmonotonic Logics

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Reasoning with Inconsistent Ontologies

• Davies et al. Ch. 5, pp 71-92
• All sections are included, but especially the
  following.
• Def. Inconsistency not consistent!
• Approaches to reasoning w/inconsistency
• Reject classical inference cannot cope with it
• Live with it apply non-standard reasoning meth.
  This chapter.
• Reasons for inconsistency
• Mis-representation of deafult
• Polysemy
• Migration from a nother formalism
• Due to multiple sources

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Sect. 5.4- Reasoning with Inconsistent
Ontologies Inconsistency Detection

• Four-Valued Logic
• Over-determined
• Accepted
• Rejected
• Undetermined

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Sect. 5.4 (continued)

• Formal definitions on Reasoning with Inconsistent
  Ontologies
• Soundness inconsistency reasoning consequences
  must be justifiable on the basis of a consistent
  subset of the theory.
• Meaningfulness an inconsistency reasoner is
  meaningfull iff all of the answers are
  meaningful.
• Local Completeness classical reasoning
  consequences are the same as inconsistency
  reasoner consequences of a subtheory.
• Maximality inconsistency reasoner computes
  exactly the consequences of a maximal consistent
  subtheory.
• Local soundness Any positive answer is also
  clasically entailed by a consistent subtheory.

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Selection Functions

• Def. An inconsistency reasoner uses a selection
  function to determine which consistent subsets
  of an inconsistent theory should be considered in
  its reasoning process.
• Given a theory ? and a query F, a selection
  function is one which returns a subset of ? in
  positive number of steps.
• Definitions
• Linear Extension Using monotonically increasing
  / decreasing selection function.
• Direct Relevance k-Relevance
• Direct Relevance to a Set
• k-Relevance
• Monotonicity

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Sect. 5.8- PION of SEKT Project

• An inconsistency reasoner based on a linear
  extension strategy and the syntactic
  (k-)relevance-based selection function from the
  SEKT Project.
• Architecture
• DIG (DL I/F for Prolog) Server Responds to
  tell ask queries
• Main control Component query analysis
• Selection Functions
• DIG Client to call external reasoner
• Ontology Repositories

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PION Architecture
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Sect. 5.8- PION (continued) Usecases

• Usecases

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Sect. 5.8- PION (continued) Testing

• Intended Answer (IA) intuitive answer
• Counter-Intuitive Answer (CIA) opposite
• Cautious Answer (CA) IA is accept/reject but
  PION returns undetermined
• Reckless Answer (RA) PION returns accept/reject
  but IA is undetermined.

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Probabilistic Reasoning

• The Ontolog Forums 5th event in the joint
  NIST-Ontolog-NCOR mini-series on "Ontology
  Measurement and Evaluation," on Thursday
  29-Mar-2007
• "Probabilistic Reasoning and Ontology Evaluation"
  with Professor Kenneth Baclawski (Northeastern
  University), Professor Kathryn Blackmond Laskey
  Dr. Paulo Costa (George Mason University), and
  Dr. Terry Janssen (Lockheed Martin). Check ppt
  and soundtrack.

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Tools for Reasoning / Inferring

• Ontology Tools Survey, Revisited by Michael Denny
• W3C Semantic Web Tools Wiki page

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Academic Conferences

• FOIS 2008 is the fifth in the series of Formal
  Ontology in Information Systems
• Saarbrücken, Germany
• Oct 31st - Nov 3rd 2008
• co-located with ISWC 2008
• Abstract/paper due date 22/24 April.
• Check topics.
• ISWC 7th International Semantic Web Conference
  (ISWC)
• ISWC 2008, Karlsruhe, Germany (Oct 26 - 30)
• Due dates Abstract/paper 9 / 16 May.

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Commercial Conferences

• The Montague Institute organizes teleconference
  roundtable discussions
• MOSS 2007 Taxonomies search (April 26, 2007).
• Social Tagging Combining folksonomies
  taxonomies (May 17, 2007).
• For other roundtables, courses, and events, see
  the Montague Institute 2008 calendar

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References

• John Davies, Rudi Studer, Paul Warren (Editors)
  Semantic Web Technologies Trends and Research in
  Ontology-based Systems, John Wiley Sons (July
  11, 2006). ISBN 0470025964. Ch. 5. pp. 71-92.
• Christopher Menzel (Texas AM University)Formal
  Ontology and Philosophical Content on the
  Semantic Web, APA Symposium on Formal Ontology
  and Philosophical Content on the Semantic Web,
  San Francisco, 28 March 2003
• (Barry Smith) Ontology, Buffalo Ontology Site.
• W3C Semantic Web Tools Wiki page
• Check Jena, SemWeb, Protégé, Swoop, etc.

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References (continued)

• The 4th event was held on Thursday 22-Feb-2007
• "Evaluating Reasoning Systems Ontology
  Languages." by Professor Michael Gruninger
  (University of Toronto, Canada) and Mr. Conrad
  Bock (NIST, USA). Speakers covered how
  ontologies, semantics, knowledge representation
  languages and logic interplay in the formal
  ontology space. Check ppt and soundtrack
• Conrad Bock, Michael Gruninger, Don Libes, Joshua
  Lubell, and Eswaran Subrahmanian Evaluating
  Reasoning Systems, NISTIR 7310 Deliverable, May
  2006, NIST, US Dept of Commerce.