Autoepistemic logic of minimal beliefs

Abstract

In recent years, various formalizations of non-monotonic 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.

We introduce a simple non-monotonic knowledge representation framework which isomorphically contains all of the above mentioned non-monotonic 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 minimal Beliefs, AELB, is obtained by augmenting Moore's autoepistemic logic, AEL, with an additional minimal belief operator, B, which allows us to explicitly talk about minimally entailed formulae.

The existence of such a uniform framework not only results in a new powerful non-monotonic formalism but also allows us to compare and better understand mutual relationships existing between different non-monotonic formalisms and semantics and enables us to provide simpler and more natural definitions of some of them. It also naturally leads to new, even more expressive and flexible formalizations and semantics.