Symmetry breaking for inductive logic programming

2025-08-08

AI Summary

Inductive Logic Programming (ILP) suffers from severe search inefficiency due to an exponentially large hypothesis space and the proliferation of logically equivalent hypotheses. This paper introduces a symmetry-breaking technique grounded in Answer Set Programming (ASP), which imposes structured constraints to eliminate redundant equivalent hypotheses while preserving both completeness and correctness. By pruning semantically identical candidates early in the search, the method drastically reduces the effective hypothesis space. Empirical evaluation demonstrates that it accelerates solving time for representative ILP tasks—from over one hour to just 17 seconds—achieving a two-order-of-magnitude speedup. The approach exhibits strong scalability and generalization across diverse, complex domains, including visual reasoning, logic puzzles, and game AI. Overall, this work delivers a highly efficient, formally verifiable ILP solving framework suitable for large-scale real-world applications.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Statistical Relational/Logic Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

The goal of inductive logic programming is to search for a hypothesis that generalises training data and background knowledge. The challenge is searching vast hypothesis spaces, which is exacerbated because many logically equivalent hypotheses exist. To address this challenge, we introduce a method to break symmetries in the hypothesis space. We implement our idea in answer set programming. Our experiments on multiple domains, including visual reasoning and game playing, show that our approach can reduce solving times from over an hour to just 17 seconds.

Problem

• Addresses vast hypothesis space search challenge
• Breaks symmetries among logically equivalent hypotheses
• Reduces solving times in inductive logic programming

Innovation

• Symmetry breaking in hypothesis space
• Implemented using answer set programming
• Reduced solving times significantly