Notes on Nonmonotonic Autoepistemic Propositional Logic

Marek A. Suchenek
2011 Zeszyty Naukowe  
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
more » ... 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.
doi:10.26348/znwwsi.6.74 doaj:c6340de35be34085b8bb73eec7d6a7e1 fatcat:li3oy2wacfgffklqj7cpniycpy