Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Castelnovo, Davide; Miculan, Marino https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-157332
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Fuzzy Algebraic Theories

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Abstract

In this work we propose a formal system for fuzzy algebraic reasoning. The sequent calculus we define is based on two kinds of propositions, capturing equality and existence of terms as members of a fuzzy set. We provide a sound semantics for this calculus and show that there is a notion of free model for any theory in this system, allowing us (with some restrictions) to recover models as Eilenberg-Moore algebras for some monad. We will also prove a completeness result: a formula is derivable from a given theory if and only if it is satisfied by all models of the theory. Finally, leveraging results by Milius and Urbat, we give HSP-like characterizations of subcategories of algebras which are categories of models of particular kinds of theories.

BibTeX - Entry

@InProceedings{castelnovo_et_al:LIPIcs.CSL.2022.13,
  author =	{Castelnovo, Davide and Miculan, Marino},
  title =	{{Fuzzy Algebraic Theories}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15733},
  URN =		{urn:nbn:de:0030-drops-157332},
  doi =		{10.4230/LIPIcs.CSL.2022.13},
  annote =	{Keywords: categorical logic, fuzzy sets, algebraic reasoning, equational axiomatisations, monads, Eilenberg-Moore algebras}
}

Keywords: categorical logic, fuzzy sets, algebraic reasoning, equational axiomatisations, monads, Eilenberg-Moore algebras
Seminar: 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)
Issue date: 2022
Date of publication: 27.01.2022


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