2008 BeliefRevisionInDescriptionLogics

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Keywords: Belief Revision, Description Logic

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Abstract

= 1 Introduction

  • Knowledge Representation and Reasoning is an established field in computing science that aims to capture and represent “knowledge” in a knowledgebase KB, allowing then to query KB to access what is explicitly stored in it and, more interestingly, what is implicitly implied by it through reasoning. The representation and reasoning is commonly carried through use of some sort of logic: propositional logic, first order logic, and description logics, to name a few.
  • Description logics, DL, have brought together highly desired aspects of many different representation formalisms. For example, on the one hand, DLs are well suited to describe and represent structural knowledge with a hierarchy of concepts similar to inheritance in the object-oriented paradigm, and on the other hand, like logical formalisms, they offer inference and reasoning capabilities. This carefully selected mixture of features has proved useful in many real life applications. (1) For example, description logics are commonly used to create ontologies – formal representation of concepts and their relationships in a particular domain. For instance, OWL, equivalent to some specific description logics, is used to build ontologies and is very heavily used in the well-known SemanticWeb drive (2).
  • Belief revision, another research field in computing science and in logic, is concerned with dynamics of an agent changing its beliefs in light of new information becoming available. The challenge is on how to incorporate a new belief into a consistent set of beliefs to create a new consistent set of beliefs containing the new belief, and as much from the old belief set as possible. A few decades of intense research has brought significant achievements to the field, although, thus far, most of the work has been theoretical.
  • Applying belief revision principles to applied logics such as description logics could be one important step forward for both fields. Belief revision in description logics is a new research area, already showing significant problem-solving capabilities, and a lot of potential to be explored and exploited. In many applications, to ensure that ontologies remain applicable to their respective problems, they need to be constantly updated and evolved. This process can be very labor intensive and error prune if carried out manually [ref]. This is where belief revision can be expected to help. Thinking of an ontology as a belief-set or knowledgebase, belief revision can be used to incorporate a new piece of information (a new belief) into the knowledgebase maintaining its consistency. This allows the initial ontology to evolve as more information becomes accessible. One encouraging observation is that the hierarchy and structural information embedded in a description logics knowledgebase could potentially be exploited to find out the parts of the knowledgebase that are relevant to a required change. If so, this would allow for relevant belief revision, which could be expected to be much more tractable on realistically large knowledgebases.
  • In this document, we will briefly introduce description logics, belief revision, belief revision in description logics, and some potential research venues in this research area.

References

1. Nardi, Daniele and Brachman, Ronald J. An Introduction to Description Logic. [book auth.] Franz Baader, et al. The Description Logic Handbook: Theory, Implementation and Applications. s.l. : Cambridge University Press, 2003. 2. Horrocks, Ian, et al. OWL: a Description-Logic-Based Ontology Language for the Semantic Web. [book auth.] Franz Baader, et al. The Description Logic Handbook: Theory, Implementation and Applications. s.l. : Cambridge University Press, 2003. 3. Baader, Franz, Horrocks, Ian and Sattler, Ulrike. Handbook of Knowledge Representation (Foundations of Artificial Intelligence). s.l. : Elsevier Science, 2007. 4. Brachman, Ronald J. and Levesque, Hector J. Structured Descriptions. Knowledge Representation and Reasoning. s.l. : Morgan Kaufmann, 2004. 5. An overview of tableau algorithms for description logics. Baader, Franz and Sattler, Ulrike. Aachen, Germany : Studia Logica, 2000. 6. Brachman, Ronald J. and Levesque, Hector J. The Tradeoff between Expressiveness and Tractability. Knowledge Representation and Reasoning. s.l. : Morgan Kaufmann, 2004. 7. Calvanese, Diego and De Giacomo, Giuseppe. Expressive Description Logics. [book auth.] Franz Baader, et al. The Description Logic Handbook: Theory, Implementation and Applications. s.l. : Cambridge University Press, 2003. 8. Web Ontology Language OWL / W3C Semantic Web Activity. [Online] The World Wide Web Consortium, (2004). http://www.w3.org/2004/OWL/. 9. A tool for automatic UML model consistency checking. Simmonds, J. and Bastarrica, M. C. s.l. : ACM New York, NY, USA, 2005. 10. Gärdenfors, Peter. Belief Revision. Lund, Sweden : Cambridge University Press, 2003. 11. Peppas, Pavlos. Belief Revision. [book auth.] F. van Harmelen, V. Lifschitz and B. Porter. Handbook of Knowledge Representation (Foundations of Artificial Intelligence). s.l. : Elsevier Science, 2007. 12. Updating DLs Using the AGM Theory: A Preliminary Study. Flouris, Giorgos, Plexousakis, Dimitris and Antoniou, Grigoris. Heraklion, Greece : Description Logics, 2006. 13. On Applying the AGM Theory to DLs and OWL. Flouris, Giorgos, Plexousakis, Dimitris and Antoniou, Grigoris. Heraklion, Greece : Lecture Notes In Computer Science, 2005. 14. First Steps Towards Revising Ontologies. Ribeiro, Marcio Moretto and Wassermann, Renata. s.l. : Proceedings of the Second Workshop on Ontologies and their Applications, 2006.

15. Description Logic Reasoning with Syntactic Updates. Halashek-Wiener, Christian, Parsia, Bijan and Sirin, Evren. s.l. : Lecture Notes In Computer Science, 2006. 16. On the Update of Description Logic Ontologies at the Instance Level. Giacomo, Giuseppe De, et al. s.l. : Proceedings Of The National Conference On Artificial Intelligence, 2006. 17. Updating Description Logic ABoxes. Liu, Hongkai, et al. s.l. : International Conference of Principles of Knowledge Representation and Reasoning, 2006. 18. Relevance sensitive belief structures. Chopra, Samir and Parikh, Rohit. s.l. : Annals of Mathematics and Artificial Intelligence, 2000. 19. Makinson, David. Propositional Relevance through Letter-Sharing: Review and Contribution. Formal Models of Belief Change in Rational Agents. s.l. : Dagstuhl Seminar Proceedings, 2007. 20. Mares, E. and Meyer, R. K. Relevant Logics. [book auth.] Lou Goble. The Blackwell Guide to Philosophical Logic. s.l. : Blackwell Publishing, 2001. 21. Propositional Relevance through Letter-Sharing: Review and Contribution. Makinson, David. Schloss Dagstuhl, Germany : Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), 2007. 22. How knowledge representation meets software engineering (and often databases). Alex, Borgida. 4, s.l. : Automated Software Engineering, 2007, Vol. 14.

 AuthorvolumeDate ValuetitletypejournaltitleUrldoinoteyear
2008 BeliefRevisionInDescriptionLogicsMehrdad OveisiBelief Revision in Description Logics: A brief overview.http://www.sfu.ca/~oveisi/DepthExam.pdf2008
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