Many-valued coalgebraic logic over semi-primal varieties
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Published:2024-07-17
Issue:
Volume:Volume 20, Issue 3
Page:
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ISSN:1860-5974
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Container-title:Logical Methods in Computer Science
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language:en
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Short-container-title:
Author:
Kurz Alexander,Poiger Wolfgang,Teheux Bruno
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.
Publisher
Centre pour la Communication Scientifique Directe (CCSD)