Belief Revision in Non-Monotonic Reasoning and Logic Programming

Abstract

In order to be able to explicitly reason about beliefs, we've introduced a non-monotonic formalism, called the Autoepistemic Logic of Beliefs, AEB, obtained by augmenting classical propositional logic with a belief operator, β. For this language we've defined the static autoepistemic expansions semantics. The resulting nonmonotonic knowledge representation framework turned out to be rather simple and yet quite powerful. Moreover, it has some very natural properties which sharply contrast with those of Moore's AEL. While static expansions seem to provide a natural and intuitive semantics for many belief theories, and, in particular, for all affirmative belief theories (which include the class of all normal and disjunctive logic programs), they often can lead to inconsistent expansions for theories in which (subjective) beliefs clash with the known (objective) information or with some other beliefs. In particular, this applies to belief theories (and to logic programs) with strong or explicit negation. In this paper we generalize AEB to avoid the acceptance of inconsistency provoking beliefs. We show how such AEB theories can be revised to prevent belief originated inconsistencies, and also to introduce declarative language level control over the revision level of beliefs, and apply it to the domains of diagnosis and declarative debugging. The generality of our AEB framework can capture and justify the methods that have been deployed to solve similar revision problems within the logic programming paradigm.