On the relation between autoepistemic logic and circumscription

Circumscription on the one hand and autoepistemic and default logics on the other seem to have quite different characteristics as formal systems, which makes it difficult to compare them as formalizations of defeasible connmonsense reasoning. In this paper we accomplish two tasks: (1) we extend the original semantics of autoepistemic logic to a language which includes variables quantified into the context of the autoepistemic operator, and (2) we show that a certain class of autoepistemic theories in the extended language has a minimal-model semantics corresponding to circumscription. We conclude that all of the first-order consequences of parallel predicate circumscription can be obtained from this class of autoepistemic theories. The correspondence we construct also sheds light on the problematic treatment of equality in circumscription.