Symmetry breaking for inductive logic programming
Andrew Cropper, David M. Cerna, Matti Järvisalo
TL;DR
This work addresses the inefficiency caused by syntactic symmetries in ILP hypothesis spaces by introducing a variable-ordering–based symmetry-breaking method for body-variant rules. Implemented inside the Popper ILP system via an ASP encoding, the approach prunes redundant rules while remaining sound, though incomplete due to GI-hardness. Empirical evaluation across visual reasoning, game-playing, and real-world domains shows substantial reductions in solving times (sometimes from over an hour to tens of seconds) and meaningful learning-time improvements, particularly as task complexity grows. The method bridges ILP and constraint programming, yielding practical speedups and highlighting both the potential and the limitations of incomplete symmetry breaking in ILP.
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.