Fuzzy Algebraic Theories

Authors Davide Castelnovo, Marino Miculan

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Author Details

Davide Castelnovo
  • Department of Mathematics, Computer Science and Physics, University of Udine, Italy
Marino Miculan
  • Department of Mathematics, Computer Science and Physics, University of Udine, Italy

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Davide Castelnovo and Marino Miculan. Fuzzy Algebraic Theories. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
  • categorical logic
  • fuzzy sets
  • algebraic reasoning
  • equational axiomatisations
  • monads
  • Eilenberg-Moore algebras


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