On Many-Valued Modal Probabilistic Logics
Ondrej Majer, Igor Sedlár · 2025
Extending Hájek’s work on propositional probabilistic logic, we introduce a semantic framework for modal probabilistic logics based on modal Łukasiewicz logic. We demonstrate the expressiveness of the framework with a number of examples. As our main technical result, we prove that, in a significant range of cases, local consequence over probabilistic models based on a class of Kripke frames reduces to parameterised local consequence over Kripke models based on that class of frames. Decidability of a number of modal probabilistic logics follows from this result.