Learning Rules with Stratified Negation in Differentiable ILP.

Differentiable methods to learn 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. While negation is an essential component of reasoning, incorporating it into a logic programming framework poses several problems (hence its central place in the logic programming and nonmonotonic reasoning communities). Current implementations of differentiable rule learners either exclude negation entirely or else treat it only in passing. In this work, we introduce stratified negation into a differentiable inductive logic programming framework, and we demonstrate that the resulting system can learn recursive programs in which negation plays a central role. We include examples from multiple domains, e.g., arithmetic, graph, sets and lists.