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GRADLACT: Graded Logics of Action

GA22-16111S [Registered results] 2022 - 2024

Propositional Dynamic Logic, PDL, is a well-known tool used in the logical analysis of discourse about action. Being based on classical logic, it cannot provide adequate formalization of discourse involving graded, vague and imprecise concepts. This project will develop and study versions of PDL more suitable for this task, so-called graded dynamic logics. We will determine the basic properties of the most natural kinds of graded dynamic logic and we will develop versions of graded PDL aiming at formalizing various philosophically relevant kinds of discourse; in particular, we will develop graded dynamic logics suitable for formalizing reasoning about collective agency and deontic aspects of action in situations involving graded notions, and for analyzing reasoning about probabilistic aspects of action. The project will thus contribute to an elaboration of formal methods applicable in the theory of action and applied ethics.