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Modal logic for default reasoning

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Abstract

In the paper we introduce a variant of autoepistemic logic that is especially suitable for expressing default reasonings. It is based on the notion of iterative expansion. We show a new way of translating default theories into the language of modal logic under which default extensions correspond exactly to iterative expansions. Iterative expansions have some attractive properties. They are more restrictive than autoepistemic expansions, and, for some classes of theories, than moderately grounded expansions. At the same time iterative expansions avoid several undesirable properties of strongly grounded expansions, for example, they are grounded in the whole set of the agent's initial assumptions and do not depend on their syntactic representation.

Iterative expansions are defined syntactically. We define a semantics which leads to yet another notion of expansion — weak iterative expansion — and we show that there is an important class of theories, that we call ℐ-programs, for which iterative and weak iterative expansions coincide. Thus, for ℐ-programs, iterative expansions can be equivalently defined by semantic means.

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Authors and Affiliations

  1. Department of Computer Science, University of Kentucky, 40506-0027, Lexington, KY, USA

    W. Marek & M. Truszczyński

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  1. W. Marek
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  2. M. Truszczyński
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Additional information

This work was partially supported by Army Research Office under grant DAAL03-89-K-0124, and by National Science Foundation and the Commonwealth of Kentucky EPSCoR program under grant RII 8610671.

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Marek, W., Truszczyński, M. Modal logic for default reasoning. Ann Math Artif Intell 1, 275–302 (1990). https://doi.org/10.1007/BF01531081

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