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Self-Supervised Inductive Logic Programming

Stassa Patsantzis

TL;DR

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.

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.

Self-Supervised Inductive Logic Programming

TL;DR

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.

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.

Paper Structure

This paper contains 30 sections, 8 theorems, 2 figures, 11 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Self-Supervised ILP by detection of contradictions
  3. Contributions
  4. Related Work
  5. Self-Supervised Learning
  6. Self-Supervised Learning in ILP
  7. Framework
  8. Meta-Interpretive Learning
  9. A Self-Supervised Learning setting for ILP
  10. Poker: an algorithm for Self-Supervised ILP
  11. Two Normal Forms
  12. Poker's algorithm
  13. Implementation
  14. Experiments
  15. Baselines
  16. ...and 15 more sections

Key Result

Theorem 1

The probability that Algorithm alg:poker returns a correct hypothesis increases monotonically with the number of unlabelled examples.

Figures (2)

  • Figure 1: Learning L-Systems: generative accuracy.
  • Figure 2: Learning CFGs. TPR: True Positive Rate. TNR: True Negative Rate.

Theorems & Definitions (18)

  • Definition 1
  • Definition 2: Constrained Metarules
  • Definition 3: Second-Order Definite Normal Form
  • Theorem 1: Hypothesis Correctness
  • Lemma 1: Generality of Initial Hypotheses
  • proof
  • Lemma 2: Correct Specialisation
  • proof
  • Lemma 3: Correct Labelling
  • proof
  • ...and 8 more