On Modal Logics for Qualitative Possibility in a Fuzzy Setting

TL;DR

This paper develops a modal logical framework for reasoning about qualitative possibility and necessity in fuzzy propositions, extending classical possibilistic logic to a many-valued fuzzy context with completeness results.

Contribution

It introduces a novel modal logic system for fuzzy possibilistic reasoning and establishes its completeness, bridging qualitative possibility with many-valued modal logics.

Findings

Established completeness of the fuzzy possibilistic modal logic

Connected qualitative possibilistic logic to many-valued modal logics MVS5 and MVKD45

Extended classical possibilistic logic results to fuzzy settings

Abstract

Within the possibilistic approach to uncertainty modeling, the paper presents a modal logical system to reason about qualitative (comparative) statements of the possibility (and necessity) of fuzzy propositions. We relate this qualitative modal logic to the many--valued analogues MVS5 and MVKD45 of the well known modal logics of knowledge and belief S5 and KD45 respectively. Completeness results are obtained for such logics and therefore, they extend previous existing results for qualitative possibilistic logics in the classical non-fuzzy setting.