Non-monotonic modal logic of belief
Michael Kaminski, Michael Tiomkin · 2007
We propose an alternative non-monotonic modal formalism called non-monotonic modal logic of belief. It is based on replacing the clas-sical fixpoint equation E = ThS(A ∪ {Mϕ: E 6`S ¬ϕ}) with the belief fixpoint equation E = ThS(A ∪ {Mϕ: E 6`S ¬Mϕ}). The so-lutions of the belief fixpoint equation, called belief S-expansions, are tightly related to the logic of belief KD45. We show interpretation of default logic in non-monotonic modal logic of belief and present minimal model semantics for belief expansions.