### 27 January 2022 14:00, CYB-101

## Speaker

**Davide Castelnovo**

## Title

Fuzzy Algebraic Theories

## Abstract

In this seminar I will present a join work with my supervisor Marino Miculan (see arxiv:2110.10970). I'll present a formal system for fuzzy algebraic reasoning: this sequent calculus is based on two kinds of propositions, capturing equality and existence of terms as members of a fuzzy set. I'll 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. I 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, if possible, I'll show how to use some results by Milius and Urbat to give an HSP-like characterizations of subcategories of algebras which are categories of models of particular kinds of theories.