Many-valued coalgebraic logic over semi-primal varieties
Logic in Computer Science
2024-08-07 v5 Category Theory
Logic
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.
Keywords
Cite
@article{arxiv.2308.14581,
title = {Many-valued coalgebraic logic over semi-primal varieties},
author = {Alexander Kurz and Wolfgang Poiger and Bruno Teheux},
journal= {arXiv preprint arXiv:2308.14581},
year = {2024}
}