Three-Values Logic and Non-Monotonic Reasoning

Abstract

In this paper we present a three-valued logical system T3 which is both sound and complete with respect to a class X partial models. We show that T3: (1) subsumes Gabbay's system m and (2) makes a distinction between two modal notions: epistemic possibility and plausibility. We then extend the class X and present Modal-T3 logics: K-T3, T-T3, S4-T3, and S5-T3. which are then analogue of standard modal logics K, T, S4 and S5 and show that all these systems are sound and complete. We also show that the explicit default operator D of Doherty [5] and of Doherty and Lukaszewicz [6] is definable in Modal-T3 and autoepistemic models [40, 41] are just a particular case of partial models modal structures.