On the Complexity of Inductively Learning Guarded Rules

TL;DR

This paper analyzes the computational complexity of learning guarded rules in inductive logic programming, establishing NP-completeness and identifying a tractable subset, with generalizations to k-guarded clauses.

Contribution

It proves NP-completeness of learning guarded clauses and introduces a natural tractable fragment, extending results to k-guarded clauses.

Findings

Learning guarded clauses is NP-complete.

A natural tractable fragment exists for large datasets.

Results extend to k-guarded clauses for constant k.

Abstract

We investigate the computational complexity of mining guarded clauses from clausal datasets through the framework of inductive logic programming (ILP). We show that learning guarded clauses is NP-complete and thus one step below the $\sigma^P_2$-complete task of learning Horn clauses on the polynomial hierarchy. Motivated by practical applications on large datasets we identify a natural tractable fragment of the problem. Finally, we also generalise all of our results to $k$-guarded clauses for constant $k$.