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Alexander Kurz ; Wolfgang Poiger ; Bruno Teheux - Many-valued coalgebraic logic over semi-primal varieties
lmcs:12384 - Logical Methods in Computer Science, July 17, 2024, Volume 20, Issue 3 - https://doi.org/10.46298/lmcs-20(3:6)2024Many-valued coalgebraic logic over semi-primal varietiesArticle
Authors: Alexander Kurz 
; Wolfgang Poiger ; Bruno Teheux
We study many-valued coalgebraic logics with semi-primal algebras of truth-degrees. We provide a systematic way to lift endofunctors defined on the variety of Boolean algebras to endofunctors on the variety generated by a semi-primal algebra. We show that this can be extended to a technique to lift classical coalgebraic logics to many-valued ones, and that (one-step) completeness and expressivity are preserved under this lifting. For specific classes of endofunctors, we also describe how to obtain an axiomatization of the lifted many-valued logic directly from an axiomatization of the original classical one. In particular, we apply all of these techniques to classical modal logic.
Source: arXiv.org:2308.14581
Volume: Volume 20, Issue 3
Secondary volumes: Selected Papers of the 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)
Published on: July 17, 2024
Accepted on: May 6, 2024
Submitted on: October 10, 2023
Keywords: Computer Science - Logic in Computer Science, Mathematics - Category Theory, Mathematics - Logic
Classifications
Mathematics Subject Classification 20201
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