Notes on Nonmonotonic Autoepistemic Propositional Logic
نویسنده
چکیده
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 minimal-knowledge 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 .
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