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Autoepistemic logic of knowledge and beliefs. (English) Zbl 0894.68141
Summary: In recent years, various formalizations of nonmonotonic reasoning and different semantics for normal and disjunctive logic programs have been proposed, including autoepistemic logic, circumscription, CWA, GCWA, ECWA, epistemic specifications, stable, well-founded, stationary and static semantics of normal and disjunctive logic programs. In this paper we introduce a simple nonmonotonic knowledge representation framework which isomorphically contains all of the above-mentioned nonmonotonic formalisms and semantics as special cases and yet is significantly more expressive than each one of these formalisms considered individually. The new formalism, called the Autoepistemic Logic of Knowledge and Beliefs, AELB, is obtained by augmenting Moore’s autoepistemic logic, AEL, already employing the knowledge operator, \({\mathcal L}\), with an additional belief operator, \(\mathcal B\). As a result, we are able to reason not only about formulae F which are known to be true (i.e., those for which \({\mathcal L}\)F holds) but also about those which are only believed to be true (i.e., those for which \(\mathcal B\)F holds). The proposed logic constitutes a powerful new formalism which can serve as a unifying framework for several major nonmonotonic formalisms. It allows us to better understand mutual relationships existing between different formalisms and semantics and enables us to provide them with simpler and more natural definitions. It also naturally leads to new, even more expressive, flexible and modular formalizations and semantics.

MSC:
68T27 Logic in artificial intelligence
68N17 Logic programming
68Q55 Semantics in the theory of computing
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