A Complete Logic for Autoepistemic Membership

The driving force behind the theory of non-monotonic reasoning is the wish to draw conclusions in the face of missing information. Therefore, one way to understand non-monotonic reasoning is to realize that not only knowledge, but also absence of knowledge enables certain conclusions. Among other theories of knowledge and ignorance, Moore's autoepistemic logic is a conscientious elaboration of this idea. However, since autoepistemic logic is in essence an introspective reasoning mechanism, the original semantics is typically stated in recursive terms. This recursion and the idiosyncratic terminology of autoepistemic semantics makes it difficult to place autoepistemic logic in the collection of existing logics of knowledge and belief. We therefore start with a brief exposition of autoepistemic logic. After this, the semantic notion of autoepistemic membership will be axiomatized. The proof system frees autoepistemic logic from a recursive semantics and molds it into a weak S 5-like moda..