Complexity of Łukasiewicz Modal Probabilistic Logics
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918221272055808 |
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| author | Kozhemiachenko, Daniil Sedlár, Igor |
| author_facet | Kozhemiachenko, Daniil Sedlár, Igor |
| contents | 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 Łukasiewicz 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_22389 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complexity of Łukasiewicz Modal Probabilistic Logics Kozhemiachenko, Daniil Sedlár, Igor Logic in Computer Science F.4.1 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 Łukasiewicz 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. |
| title | Complexity of Łukasiewicz Modal Probabilistic Logics |
| topic | Logic in Computer Science F.4.1 |
| url | https://arxiv.org/abs/2511.22389 |