Graded Relation Updates in Modal Logic

Raul Fervari, Daniel Figueiredo, Manuel A. Martins

Abstract: This paper introduces a fuzzy approach to modal logics with graded relation updates. Specifically, we develop relation-changing modal logics where modalities modify the membership degree of a pair of elements in the accessibility relation. Our framework encompasses variants of local swap, sabotage, and bridge modalities. We motivate our approach via examples, and provide bisimulation notions for each logic, together with their corresponding characterization theorems. We also prove that model-checking for these logics is \(\textsf{PSpace}\)-complete, exactly as in the non-fuzzy cases.