Autoepistemic circumscription and logic programming

Abstract

We propose a framework of autoepistemic reasoning in which the underlying semantics is determined by the choice of a nonmonotonic inference mechanism and by specifying abelief constraint. While the latter makes the approach flexible in meeting possibly different applications, the former links the resulting semantics to a nonmonotonic reasoning formalism and thus allows adoption of existing techniques. In this paper we choosecircumscription as the underlying inference mechanism and use two different belief constraints to define two semantics,the stable circumscriptive semantics andthe well-founded circumscriptive semantics, for autoepistemic theories. The former coincides with Moore's autoepistemic logic for logic programs and is arguably more desirable in handling disjunctive autoepistemic theories. The latter is a reconstruction and extension of Przymusinski's iterative method for computing the leastAEL(circ) expansions for logic programs. We show that for logic programs the two construction methods coincide. However, while Przymusinski's construction method is restricted to logic programs only, the well-founded circumscriptive semantics is applicable to more general autoepistemic theories.