Exploit Domain Knowledge: Smarter Abductive Learning and Its Application to Math Word Problems

Perception and reasoning are two representative abilities of intelligence, and Abductive Learning (ABL) is targeted at unifying the two abilities in a mutually beneficial way, where the neural model learns to perceive the primitive logic facts from raw data, and logical reasoning can exploit domain knowledge to correct the wrongly perceived facts for training the neural model. However, there are three flaws in ABL: (1) While logical reasoning corrects the wrongly perceived facts, the corrected facts may contain redundancy. (2) Some complex facts are hard to correct, therefore no supervision can be provided by the corresponding samples in dataset. (3) The correction of logical reasoning induces a large number of spurious facts, which degrades the performance of the model. In this paper, we focus on these issues and argue that the lack of overall exploitation of domain knowledge is the root cause. We propose a Smarter Abductive Learning (S-ABL) framework. In this framework, we first sum up some extra knowledge and propose three mechanisms via extra knowledge, namely simplification, filtration, augmentation. We exploit the extra knowledge to simplify, filter and augment corrected facts to improve the quality and quantity of the corrected facts. The effectiveness of our framework has been verified in the math word problem. We experiment on dataset Math23k and MAWPS. In weak supervision, our method achieves 64.8% and 52.9% accuracy, outperforming the existing baseline by 5.4% points and 7.3% points on dataset Math23k and MAWPS respectively.