Stable belief sets revisited

Authors:
Costas D. Koutras;Yorgos Zikos
Affiliations:
Department of Computer Science and Technology, University of Peloponnese, Tripolis, Greece;Graduate Programme in Logic, Algorithms and Computation, Department of Mathematics, University of Athens, Ilissia, Greece
Venue:
JELIA'10 Proceedings of the 12th European conference on Logics in artificial intelligence
Year:
2010

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Abstract

Stable belief sets were introduced by R. Stalnaker in the early '80s, as a formal representation of the epistemic state for an ideal introspective agent. This notion motivated Moore's autoepistemic logic and greatly influenced modal nonmonotonic reasoning. Stalnaker stable sets possess an undoubtly simple and intuitive definition and can be elegantly characterized in terms of S5 universal models or KD45 situations. However, they do model an extremely perfect introspective reasoner and suffer from a Knowledge Representation (KR) version of the logical omniscience problem. In this paper, we vary the context rules underlying the positive and/or negative introspection conditions in the original definition of R. Stalnaker, to obtain variant notions of a stable epistemic state, which appear to be more plausible under the epistemic viewpoint. For these alternative notions of stable belief set, we obtain representation theorems using possible world models with non-normal (impossible) worlds and neighborhood modal models.