Reasoning About Probabilities, Actions, and Knowledge in Fuzzy Modal Logic
It provides a formal framework for combining probabilistic, epistemic, and dynamic reasoning, but the results are incremental as they extend existing modal logics with probability measures.
The paper introduces a fuzzy modal logic for reasoning about probabilities, actions, and knowledge, and analyzes the complexity of satisfiability, identifying fragments decidable in polynomial time.
We explore a fuzzy modal logic that can formalise probabilistic reasoning about actions and knowledge. In particular, we deal with contexts involving statements about events expressed via modal formulas, e.g., "after doing $a$, the probability of $A$ knowing that $p$ holds increases / decreases / is equal to $0.25$", "according to $A$, $p$ is equally likely to happen after doing $a$ or $b$", etc. We define the semantics of the logic on Kripke frames equipped with probability measures. We analyse the complexity of deciding the satisfiability of formulas of our logic over finitely branching models, for the full language and its fragments of varying expressivity. In particular, we identify several fragments of our logic where satisfiability is decidable in polynomial time.