A Fuzzy Modal Logic for Fuzzy Transition Systems

Abstract

This paper intends to contribute with a new fuzzy modal logic to model and reason about transition systems involving uncertainty in behaviours. Our formalism supports fuzziness at transitions and on the proposition symbols assignment levels.

Against of other approaches in the literature, our bisimulation and bisimilarity notions generalise the analogous standard notions of classic modal logic and of process algebras. Moreover, the outcome of our logic is also fuzzy, with the semantic interpretation of connectives supported by the Gödel algebra.