# Intellectics Group: Technical Report 96-19

## Improving Theories for Inductive Logic Programming
Systems with Ground Reduced Programs

### Akihiro Yamamoto

In this paper we improve the theory of inverse entailment given by Muggleton.
The theory of inverse entailment is a foundation of the Progol system,
one of the most famous ILP systems.
We first point out that the theory is incomplete in general.
Secondly we prove that the theory is complete if the background knowledge
given to the system is a ground reduced program, every training example
is a ground unit clause, and the hypothesis space is the set
of all definite clauses.
The proof is obtained by showing that every ground reduced logic program
is logically equivalent to the conjunction of all atoms in its least model.
As a corollary to this equivalence, we are finally able to improve the
theory for the GOLEM system.