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

TL;DR

This paper introduces a simplified possibilistic semantics for the modal logic KD45(G), a many-valued G"odel extension of classical modal logic, using possibilistic G"odel Kripke frames to characterize valid formulas.

Contribution

It provides a novel simplified semantics for KD45(G) by characterizing it through possibilistic G"odel Kripke frames, bridging fuzzy logic and modal logic.

Findings

Characterization of KD45(G) via possibilistic G"odel Kripke frames

Simplified semantics for a many-valued modal logic

Connection between fuzzy logic and modal logic validity

Abstract

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. More precisely, we characterize KD45(G) as the set of valid formulae of the class of possibilistic G\"odel Kripke Frames $\langle W,\pi \rangle$, where $W$ is a non-empty set of worlds and $\pi: W \longrightarrow [0, 1]$ is a normalized possibility distribution on $W$.