[2308.14581] Many-valued coalgebraic logic over semi-primal varieties
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arXiv:2308.14581 (cs)
[Submitted on 28 Aug 2023 (v1), last revised 16 Jul 2024 (this version, v5)]

Title:Many-valued coalgebraic logic over semi-primal varieties

Authors:Alexander Kurz, Wolfgang Poiger, Bruno Teheux
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Abstract: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.
Subjects: Logic in Computer Science (cs.LO); Category Theory (math.CT); Logic (math.LO)
Cite as: arXiv:2308.14581 [cs.LO]
  (or arXiv:2308.14581v5 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2308.14581
Journal reference: Logical Methods in Computer Science, Volume 20, Issue 3 (July 17, 2024) lmcs:12384
Related DOI: https://doi.org/10.46298/lmcs-20%283%3A6%292024

Submission history

From: Wolfgang Poiger [view email] [via LMCS proxy]
[v1] Mon, 28 Aug 2023 13:47:36 UTC (34 KB)
[v2] Mon, 9 Oct 2023 11:24:09 UTC (412 KB)
[v3] Fri, 12 Apr 2024 12:47:21 UTC (45 KB)
[v4] Wed, 8 May 2024 11:01:13 UTC (51 KB)
[v5] Tue, 16 Jul 2024 16:10:43 UTC (52 KB)
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