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DOI: 10.4230/LIPIcs.CALCO.2023.17

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

Authors: Alexander Kurz and Wolfgang Poiger

Published in: LIPIcs, Volume 270, 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)

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.

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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)

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@InProceedings{kurz_et_al:LIPIcs.CALCO.2023.17,
  author =	{Kurz, Alexander and Poiger, Wolfgang},
  title =	{{Many-Valued Coalgebraic Logic: From Boolean Algebras to Primal Varieties}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-287-7},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{270},
  editor =	{Baldan, Paolo and de Paiva, Valeria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2023.17},
  URN =		{urn:nbn:de:0030-drops-188147},
  doi =		{10.4230/LIPIcs.CALCO.2023.17},
  annote =	{Keywords: coalgebraic modal logic, many-valued logic, primal algebras, algebraic semantics, presenting functors}
}

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

Abstract

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