Simplified Kripke semantics for K45-like Godel modal logics and its axiomatic extensions

TL;DR

This paper introduces a simplified semantics for the Godel version of the modal logic K45, using possibilistic Kripke frames to characterize valid formulas in a many-valued setting.

Contribution

It provides a novel simplified semantics for K45(G) using possibilistic Kripke frames, extending classical modal logic to a many-valued Godel context.

Findings

Characterization of K45(G) via possibilistic Godel Kripke frames

Simplification of semantics for Godel modal logic K45(G)

Extension of classical modal logic to a many-valued framework

Abstract

In this paper, we provide simplified semantics for the logic K45(G), i.e. the many-valued Godel counterpart of the classical modal logic K45. More precisely, we characterize K45(G) as the set of valid formulae of the class of possibilistic Godel Kripke Frames <W,\pi> where W is a non-empty set of worlds and \pi: W \to [0, 1] is a possibility distribution on W.