Learning Rules with Stratified Negation in Differentiable ILP.

Abstract

Differentiable methods to learn first order rules (logic programs) have the potential to integrate the interpretability, transferability and low data requirements of inductive logic programming with the noise tolerance of non-symbolic learning.Negation is an essential component of reasoning, but incorporating it into logic programming frameworks poses several problems (hence its central place in the logic programming and nonmonotonic reasoning communities). Current implementations of differentiable rule learners do not learn rules with negations. Here,we introduce stratified negation into a differentiable inductive logic programming framework, and we demonstrate that the resulting system can learn recursive pro-grams with inventive predicates in which negation plays a central role. We include examples from multiple domains, e.g., arithmetic, graph, sets and lists.