Safe Abductive Learning in the Presence of Inaccurate Rules

Integrating complementary strengths of raw data and logical rules to improve the learning generalization has been recently shown promising and effective, e.g., abductive learning is one generic framework that can learn the perception model from data and reason between rules simultaneously. However, the performance would be seriously decreased when inaccurate logical rules appear, which may be even worse than baselines using only raw data. Efforts on this issue are highly desired while remain to be limited. This paper proposes a simple and effective safe abductive learning method to alleviate the harm caused by inaccurate rules. Unlike the existing methods which directly use all rules without correctness checks, it utilizes them selectively by constructing a graphical model with an adaptive reasoning process to prevent performance hazards. Theoretically, we show that induction and abduction are mutually beneficial, and can be rigorously justified from a classical maximum likelihood estimation perspective. Experiments on diverse tasks show that our method can tolerate at least twice as many inaccurate rules as accurate ones and achieve highly competitive performance while other methods can't. Moreover, the proposal can refine inaccurate rules and works well in extended weakly supervised scenarios.