Self-Supervised Inductive Logic Programming

TL;DR

This paper introduces a self-supervised approach to Inductive Logic Programming that learns from positive and unlabelled data without expert-provided background theories or negative examples, using a new MIL algorithm and system called Poker.

Contribution

It formalizes a new self-supervised ILP setting, develops a novel MIL algorithm and system, and proposes a general second-order background theory to enhance learning without expert input.

Findings

Poker outperforms Louise on grammar learning tasks.

Performance of Poker improves with more generated examples.

Louise over-generalizes without negative examples.

Abstract

Inductive Logic Programming (ILP) approaches like Meta \-/ Interpretive Learning (MIL) can learn, from few examples, recursive logic programs with invented predicates that generalise well to unseen instances. This ability relies on a background theory and negative examples, both carefully selected with expert knowledge of a learning problem and its solutions. But what if such a problem-specific background theory or negative examples are not available? We formalise this question as a new setting for Self-Supervised ILP and present a new MIL algorithm that learns in the new setting from some positive labelled, and zero or more unlabelled examples, and automatically generates, and labels, new positive and negative examples during learning. We implement this algorithm in Prolog in a new MIL system, called Poker. We compare Poker to state-of-the-art MIL system Louise on experiments learning grammars for Context-Free and L-System languages from labelled, positive example strings, no negative examples, and just the terminal vocabulary of a language, seen in examples, as a first-order background theory. We introduce a new approach for the principled selection of a second-order background theory as a Second Order Definite Normal Form (SONF), sufficiently general to learn all programs in a class, thus removing the need for a backgound theory tailored to a learning task. We find that Poker's performance improves with increasing numbers of automatically generated examples while Louise, bereft of negative examples, over-generalises.