Mapping to Declarative Knowledge for Word Problem Solving

TL;DR

This paper introduces a framework that uses declarative knowledge rules to improve the interpretability and accuracy of solving math word problems by mapping natural language to mathematical expressions.

Contribution

It develops a novel method that incorporates declarative rules into word problem solving, enabling better handling of multiple concepts and improved generalization.

Findings

Outperforms existing systems in accuracy.

Generalizes better with biased training data.

Supports interpretability of solutions.

Abstract

Math word problems form a natural abstraction to a range of quantitative reasoning problems, such as understanding financial news, sports results, and casualties of war. Solving such problems requires the understanding of several mathematical concepts such as dimensional analysis, subset relationships, etc. In this paper, we develop declarative rules which govern the translation of natural language description of these concepts to math expressions. We then present a framework for incorporating such declarative knowledge into word problem solving. Our method learns to map arithmetic word problem text to math expressions, by learning to select the relevant declarative knowledge for each operation of the solution expression. This provides a way to handle multiple concepts in the same problem while, at the same time, support interpretability of the answer expression. Our method models the mapping to declarative knowledge as a latent variable, thus removing the need for expensive annotations. Experimental evaluation suggests that our domain knowledge based solver outperforms all other systems, and that it generalizes better in the realistic case where the training data it is exposed to is biased in a different way than the test data.