We study many-valued coalgebraic logics with primal algebras of truth-degrees. We describe a way to lift algebraic semantics of classical coalgebraic logics, given by an endofunctor on the variety of Boolean algebras, to this many-valued setting, and we show that many important properties of the original logic are inherited by its lifting. Then, we deal with the problem of obtaining a concrete axiomatic presentation of the variety of algebras for this lifted logic, given that we know one for the original one. We solve this problem for a class of presentations which behaves well with respect to a lattice structure on the algebra of truth-degrees.
A. Kurz and W. Poiger. Many-valued coalgebraic logic: From boolean algebras to primal varieties. Leibniz International Proceedings in Informatics (LIPIcs), 270:17, 2023. 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). https://doi.org/10.4230/LIPIcs.CALCO.2023.17
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