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Default reasoning by deductive planning

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Abstract

This paper deals with the automation of reasoning from incomplete information by means of default logics. We provide proof procedures for default logics' major reasoning modes, namely, credulous and skeptical reasoning. We start by reformulating the task of credulous reasoning in default logics as deductive planning problems. This interpretation supplies us with several interesting and valuable insights into the proof theory of default logics. Foremost, it allows us to take advantage of the large number of available methods, algorithms, and implementations for solving deductive planning problems. As an example, we demonstrate how credulous reasoning in certain variants of default logic is implementable by means of a planning method based on equational logic programming. In addition, our interpretation allows us to transfer theoretical results, such as complexity results, from the field of planning to that of default logics. In this way, we have isolated two yet unknown classes of default theories for which deciding credulous entailment is polynomial.

Our approach to skeptical reasoning relies on an arbitrary method for credulous reasoning. It does not strictly require rather the inspection of all extensions, nor does it strictly require the computation of entire extensions to decide whether a formula is skeptically entailed. Notably, our approach abstracts from an underlying credulous reasoner. In this way, it can be used to extend existing formalisms for credulous reasoning to skeptical reasoning.

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Authors and Affiliations

  1. FG Intellektik, TH Darmstadt, Alexanderstraße 10, D-64283, Darmstadt, Germany

    Michael Thielscher

  2. IRISA, Campus de Beaulieu, F-35042, Rennes Cedex, France

    Torsten Schaub

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  1. Michael Thielscher
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  2. Torsten Schaub
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This author was a visiting professor at the University of Darmstadt while parts of this work were being carried out. This author also acknowledges support from the Commission of the European Communities under grant no. ERB4001GT922433.

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Thielscher, M., Schaub, T. Default reasoning by deductive planning. J Autom Reasoning 15, 1–40 (1995). https://doi.org/10.1007/BF00881829

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