# Axiomatisability and hardness for universal Horn classes of hypergraphs

## TL;DR

This paper investigates the conditions under which universal Horn classes of hypergraphs can be finitely axiomatized and determines the computational difficulty of membership decision problems.

## Contribution

It provides a characterization of finite axiomatisability and intractability for universal Horn classes generated by finite loop-free hypergraphs.

## Key findings

- Finite axiomatisability characterized
- Deciding membership is intractable in general
- Conditions for tractability identified

## Abstract

We characterise finite axiomatisability and intractability of deciding membership for universal Horn classes generated by finite loop-free hypergraphs.