Journal of Automated Reasoning

, Volume 14, Issue 1, pp 149–180 | Cite as

Embedding defaults into terminological knowledge representation formalisms

  • Franz Baader
  • Bernhard Hollunder
Article

Abstract

We consider the problem of integrating Reiter's default logic into terminological representation systems. It turns out that such an integration is less straightforward than we expected, considering the fact that the terminological language is a decidable sublanguage of first-order logic. Semantically, one has the unpleasant effect that the consequences of a terminological default theory may be rather unintuitive, and may even vary with the syntactic structure of equivalent concept expressions. This is due to the unsatisfactory treatment of open defaults via Skolemization in Reiter's semantics. On the algorithmic side, we show that this treatment may lead to an undecidable default consequence relation, even though our base language is decidable, and we have only finitely many (open) defaults. Because of these problems, we then consider a restricted semantics for open defaults in our terminological default theories: default rules are applied only to individuals that are explicitly present in the knowledge base. In this semantics it is possible to compute all extensions of a finite terminological default theory, which means that this type of default reasoning is decidable. We describe an algorithm for computing extensions and show how the inference procedures of terminological systems can be modified to give optimal support to this algorithm.

Key words

knowledge representation terminological reasoning nonmonotonic reasoning default logic 

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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Franz Baader
    • 1
  • Bernhard Hollunder
    • 2
  1. 1.Lehr- und Forschungsgebiet Theoretische InformatikRWTH AachenAachenGermany
  2. 2.Deutsches Forschungszentrum für KI (DFKI)SaarbrückenGermany

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