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Many-Valued Coalgebraic Logic: From Boolean Algebras to Primal Varieties

Authors Alexander Kurz, Wolfgang Poiger

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Author Details

Alexander Kurz
  • Fowler School of Engineering, Chapman University, Orange, CA, USA
Wolfgang Poiger
  • Department of Mathematics, University of Luxembourg, Esch-sur-Alzette, Luxembourg

Funding

  • Poiger, Wolfgang: Supported by the Luxembourg National Research Fund under the project PRIDE17/12246620/GPS.

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Alexander Kurz and Wolfgang Poiger. Many-Valued Coalgebraic Logic: From Boolean Algebras to Primal Varieties. In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CALCO.2023.17

Abstract

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
  • Theory of computation → Categorical semantics
  • Theory of computation → Algebraic semantics
Keywords
  • coalgebraic modal logic
  • many-valued logic
  • primal algebras
  • algebraic semantics
  • presenting functors

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