Possibilistic semantics for a modal KD45 extension of Gödel fuzzy logic

preprint2016arXivOpen access

Abstract

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

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