Heuristic Based Induction of Answer Set Programs: From Default theories to combinatorial problems

TL;DR

This paper introduces a novel heuristic ILP algorithm capable of inducing non-monotonic answer set programs with multiple stable models, enabling the solution of complex combinatorial problems more efficiently.

Contribution

It extends previous ILP methods to learn arbitrary answer set programs with multiple stable models using a greedy algorithm, improving scalability and expressiveness.

Findings

First heuristic ILP for multi-stable answer set programs

Successfully applied to graph-coloring and N-queens problems

Demonstrates improved scalability over exhaustive methods

Abstract

Significant research has been conducted in recent years to extend Inductive Logic Programming (ILP) methods to induce Answer Set Programs (ASP). These methods perform an exhaustive search for the correct hypothesis by encoding an ILP problem instance as an ASP program. Exhaustive search, however, results in loss of scalability. In addition, the language bias employed in these methods is overly restrictive too. In this paper we extend our previous work on learning stratified answer set programs that have a single stable model to learning arbitrary (i.e., non-stratified) ones with multiple stable models. Our extended algorithm is a greedy FOIL-like algorithm, capable of inducing non-monotonic logic programs, examples of which includes programs for combinatorial problems such as graph-coloring and N-queens. To the best of our knowledge, this is the first heuristic-based ILP algorithm to induce answer set programs with multiple stable models.