Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its Axiomatic Extensions

Abstract In this paper we provide a simplified, possibilistic semantics for the logics K45( G ), i.e. many-valued counterpart of classical modal logic K45 over [0, 1]-valued Gödel fuzzy $$\mathbf{G}$$ G . More precisely, characterize ) as set valid formulae class frames $$\langle W, \pi \rangle $$ ⟨ W , π ⟩ , where W is non-empty worlds and $$\pi : \mathop {\rightarrow }[0,1]$$ : → [ 0 1 ] possibility distribution on We decidability results well. Moreover, show that all also apply to extension with axiom (D), provided restrict ourselves normalised Kripke frames, satisfies normalisation condition $$\sup _{w \in W} (w) = 1$$ sup w ∈ ( ) =