Non-monotonic modal logic of belief

We propose an alternative non-monotonic modal formalism called non-monotonic modal logic of belief. It is based on replacing the classical fixpoint equation E = ThS(A ∪ {Mφ : E 6`S ¬φ}) with the belief fixpoint equation E = ThS(A ∪ {Mφ : E 6`S ¬Mφ}). The solutions 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.