Technical Report CS-2007-04

Title: Non-monotonic modal logic of belief
Authors: Michael Kaminski and Michael Tiomkin
Abstract: We propose an alternative non-monotonic modal formalism called {\em non-monotonic modal logic of belief}. It is based on replacing the classical fixpoint equation $\E = \Th_{\sS}(A \cup \{ M\varphi : \E \not\vdash_{\sS} \neg\varphi \})$ with the {\em belief} fixpoint equation $\E = \Th_{\sS} (A \cup \{ M\varphi : \E \not\vdash_{\sS} \neg M\varphi \})$. The solutions of the belief fixpoint equation, called {\em 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.

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