Possibilistic Semantics for a Modal KD45 Extension of Gödel Fuzzy Logic

In this paper we provide a simplified semantics for the logic \(KD45(\mathbf {G})\), i.e. the many-valued Godel counterpart of the classical modal logic KD45. More precisely, we characterize \(KD45(\mathbf {G})\) as the set of valid formulae of the class of possibilistic Godel Kripke Frames \(\langle W, \pi \rangle \), where W is a non-empty set of worlds and \(\pi : W \rightarrow [0, 1]\) is a normalized possibility distribution on W.