Fuzzy Algebraic Theories
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.
Keywords
Cite
@article{arxiv.2110.10970,
title = {Fuzzy Algebraic Theories},
author = {Davide Castelnovo and Marino Miculan},
journal= {arXiv preprint arXiv:2110.10970},
year = {2021}
}