# Term Models of Horn Clauses over Rational Pavelka Predicate Logic

## TL;DR

This paper investigates the universal Horn fragment of Rational Pavelka predicate logic, establishing the existence of free models and their properties for theories of Horn clauses in this fuzzy logic framework.

## Contribution

It introduces the notion of term structures for theories over Rational Pavelka logic and proves their freeness and model properties for Horn clause theories.

## Key findings

- Existence of free models for Horn clause theories
- Construction of term structures as models of Horn theories
- Validation that term structures satisfy Horn clause theories

## Abstract

This paper is a contribution to the study of the universal Horn fragment of predicate fuzzy logics, focusing on the proof of the existence of free models of theories of Horn clauses over Rational Pavelka predicate logic. We define the notion of a term structure associated to every consistent theory T over Rational Pavelka predicate logic and we prove that the term models of T are free on the class of all models of T. Finally, it is shown that if T is a set of Horn clauses, the term structure associated to T is a model of T.