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In this paper we provide a simplified semantics for the logic KD45(G), i.e.the many-valued G\"odel counterpart of the classical modal logic KD45. Moreprecisely, we characterize KD45(G) as the set of valid formulae of the class ofpossibilistic G\"odel Kripke Frames $\langle W,\pi \rangle$, where $W$ is anon-empty set of worlds and $\pi: W \longrightarrow [0, 1]$ is a normalizedpossibility distribution on $W$.

Possibilistic semantics for a modal KD45 extension of G\"odel fuzzy logic