Embedding Defaults into Terminological Representation Systems

Franz BaaderFranz Baader, B. HollunderB. Hollunder

Datei:DFKI-RR-93-20.ps.gz

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Franz Baader, B. Hollunder
Embedding Defaults into Terminological Representation Systems
Technical Report, Deutsches Forschungszentrum für Künstliche Intelligenz, Kaiserslautern, volume {RR}-93-20, 1993. {DFKI} Research Report

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KurzfassungAbstract
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 only applied 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.
Forschungsgruppe:Research Group: AutomatentheorieAutomata Theory

@techreport{ DFKI-RR-93-20,
  author = {F. {Baader} and B. {Hollunder}},
  institution = {{D}eutsches {F}orschungszentrum f\"ur {K}\"unstliche {I}ntelligenz, Kaiserslautern},
  number = {{RR}-93-20},
  title = {Embedding Defaults into Terminological Representation Systems},
  type = {{DFKI} Research Report},
  year = {1993},
}