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arXiv · 2511.22389

Complexity of {\L}ukasiewicz Modal Probabilistic Logics

Daniil Kozhemiachenko·Igor Sedlár
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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.

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Daniil Kozhemiachenko, Igor Sedlár. 2025-11-27. Complexity of {\L}ukasiewicz Modal Probabilistic Logics. https://doi.org/10.4204/eptcs.437.28

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