Complexity of Łukasiewicz Modal Probabilistic Logics

Modal probabilistic logics provide a framework for reasoning about probability in modal contexts, involving notions such as knowledge, belief, time, and action.In this paper, we study a particular family of these logics, extending the modal ukasiewicz many-valued logic.These logics are shown to be capable of expressing nuanced probabilistic concepts, including upper and lower probabilities.Our main contribution is a PSPACE-completeness result for two variants of the local consequence problem, providing a precise computational characterisation.