# Truth-preservation under fuzzy pp-formulas

## TL;DR

This paper explores how non-classical fuzzy logic can be used to analyze the complexity of fuzzy constraint satisfaction problems through a model-theoretic approach, providing algebraic characterizations of certain logical classes.

## Contribution

It introduces an algebraic characterization of classes defined by fuzzy positive-primitive sentences, advancing understanding of fuzzy logic's role in complexity analysis.

## Key findings

- Algebraic characterization of fuzzy positive-primitive classes
- Use of homomorphisms and direct products in analysis
- Insights into expressiveness of non-classical languages

## Abstract

How can non-classical logic contribute to the analysis of complexity in computer science? In this paper, we give a step towards this question, taking a logical model-theoretic approach to the analysis of complexity in fuzzy constraint satisfaction. We study fuzzy positive-primitive sentences, and we present an algebraic characterization of classes axiomatized by this kind of sentences in terms of homomorphisms and direct products. The ultimate goal is to study the expressiveness and reasoning mechanisms of non-classical languages, with respect to constraint satisfaction problems and, in general, in modelling decision scenarios. fuzzy constraint satisfaction, fuzzy logics, model theory.