Autoepistemic Logic of Knowledge and Beliefs

In recent years, various formalizations of non-monotonic reasoning and diierent semantics for normal and disjunctive logic programs have been proposed, including autoepistemic stationary and static semantics of normal and disjunctive logic programs. In this paper 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 signiicantly 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, L, with an additional belief operator, 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 LF holds) but also about those which are only believed to be true (i.e., those for which BF holds). The proposed logic constitutes a powerful new formalism which can serve as a unifying framework for several major non-monotonic formalisms. It allows us to better understand mutual relationships existing between diierent formalisms and semantics and enables us to provide them with simpler and more natural deenitions. It also naturally leads to new, even more expressive, exible and modular formalizations and semantics.