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Fuzzy Algebraic Theories Castelnovo, Davide Miculan, Marino categorical logic fuzzy sets algebraic reasoning equational axiomatisations monads Eilenberg-Moore algebras 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Davide Castelnovo and Marino Miculan 2022 Is Part Of LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2022.13 urn:nbn:de:0030-drops-157332 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.13 eng https://creativecommons.org/licenses/by/4.0/legalcode