Possible-World Semantics for Autoepistemic Logic

Abstract : In a previous paper [Moore, 1983a, 1983b], we presented a nonmonotonic logic for modeling the beliefs of ideally rational agents who reflect on their own beliefs, which we called "autoepistemic logic." We defined a simple and intuitive semantics for autoepistemic logic and proved the logic sound and complete with respect to that semantics. However, the nonconstructive character of both the logic and its semantics made it difficult to prove the existence of sets of beliefs satisfying all the constraints of autoepistemic logic. This note presents an alternative, possible-world semantics for autoepistemic logic that enables us to construct finite models for autoepistemic theories, as well as to demonstrate the existence of sound and complete autoepistemic theories based on given sets of premises.