# On the existence of Free Models in Fuzzy Universal Horn Classes

## TL;DR

This paper investigates the existence of free models within fuzzy universal Horn classes, establishing foundational results about Herbrand models in fuzzy logic programming.

## Contribution

It introduces the concept of term structures in fuzzy logic and proves the existence of free models and Herbrand models for certain fuzzy theories.

## Key findings

- Existence of free models in fuzzy universal Horn classes
- Every equality-free consistent universal Horn fuzzy theory has a Herbrand model
- Introduction of term structures in fuzzy logic context

## Abstract

This paper is a contribution to the study of the universal Horn fragment of predicate fuzzy logics, focusing on some relevant notions in logic programming. We introduce the notion of term structure associated to a set of formulas in the fuzzy context and we show the existence of free models in fuzzy universal Horn classes. We prove that every equality-free consistent universal Horn fuzzy theory has a Herbrand model.