Complexity of {\L}ukasiewicz Modal Probabilistic Logics

TL;DR

This paper investigates a family of modal { extL}ukasiewicz probabilistic logics, demonstrating their expressive power for probabilistic reasoning and establishing their computational complexity as PSPACE-complete for certain inference problems.

Contribution

It introduces a new family of modal { extL}ukasiewicz probabilistic logics and proves PSPACE-completeness for key consequence problems, advancing understanding of their computational properties.

Findings

Expressive power for probabilistic concepts like upper and lower probabilities

PSPACE-completeness of local consequence problem variants

Precise computational characterization of these logics

Abstract

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 {\L}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.