On Modal Logics for Qualitative Possibility in a Fuzzy Setting
This work addresses uncertainty modeling for researchers in fuzzy logic and modal logic, but it is incremental as it builds on existing frameworks.
The paper tackles the problem of reasoning about qualitative possibility and necessity of fuzzy propositions by presenting a modal logical system, and it achieves completeness results that extend previous work in non-fuzzy settings.
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.