Notes on Nonmonotonic Autoepistemic Propositional Logic

Abstract

This paper comprises an in-depth study of semantics of autoepistemic logic that is based on author’s may years of research in the subject matter. It begins with a brief review of semantics of common patterns of nonmonotonic deduction arising from a lack of knowledge, including autoepistemic deduction, in terms of the fixed-point equation φ(T,E)=E. Then it narrowly investigates minimal expansion semantics for autoepistemic propositional logic and its „only knowing” consequence operation CnAE. In particular, the following minimalknowledge assumption MKA : ϕ∈MKA(T) iff ϕ does not add modally positive S5- consequences to T is used to syntactically characterize the operation CnAE by means of suitable completeness theorem. The paper also offers a proof that the consequence operation CnS5 of modal logic S5 is the maximal monotonic consequence operation satisfying CnS5(T)⊆MKA(T) for every modal theory T.