Mapping to Declarative Knowledge for Word Problem Solving

Mapping to Declarative Knowledge for Word Problem Solving Subhro Roy∗ Massachusetts Institute of Technology subhro@csail.mit.edu Dan Roth∗ University of Pennsylvania danroth@seas.upenn.edu Abstract Math word problems form a natural abstrac- tion to a range of quantitative reasoning prob- lems, such as understanding financial news, sports results, and casualties of war. Solving such problems requires the understanding of several mathematical concepts such as dimen- sional analysis, subset relationships, etc. In this paper, we develop declarative rules which govern the translation of natural language de- scription of these concepts to math expres- sions. We then present a framework for in- corporating such declarative knowledge into word problem solving. Our method learns to map arithmetic word problem text to math ex- pressions, 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 prob- lem while, at the same time, supporting in- terpretability of the answer expression. Our method models the mapping to declarative knowledge as a latent variable, thus remov- ing the need for expensive annotations. Exper- imental 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 ex- posed to is biased in a different way than the test data. 1 Introduction Many natural language understanding situations re- quire reasoning with respect to numbers or quanti- ∗Most of the work was done when the authors were at the University of Illinois, Urbana Champaign. ties – understanding financial news, sports results, or the number of casualties in a bombing. Math word problems form a natural abstraction to a lot of these quantitative reasoning problems. Conse- quently, there has been a growing interest in devel- oping automated methods to solve math word prob- lems (Kushman et al., 2014; Hosseini et al., 2014; Roy and Roth, 2015). Arithmetic Word Problem Mrs. Hilt baked pies last weekend for a holiday din- ner. She baked 16 pecan pies and 14 apple pies. If she wants to arrange all of the pies in rows of 5 pies each, how many rows will she have? Solution (16 + 14)/5 = 6 Math Concept needed for Each Operation Figure 1: An example arithmetic word problem and its solution, along with the concepts required to generate each operation of the solution Understanding and solving math word problems involves interpreting the natural language descrip- tion of mathematical concepts, as well as under- standing their interaction with the physical world. Consider the elementary school level arithmetic word problem shown in Fig 1. To solve the prob- lem, one needs to understand that “apple pies” and “pecan pies” are kinds of “pies”, and hence, the 159 Transactions of the Association for Computational Linguistics, vol. 6, pp. 159–172, 2018. Action Editor: Luke Zettlemoyer. Submission batch: 10/2017; Revision batch: 12/2017; Published 3/2018. c⃝2018 Association for Computational Linguistics. Distributed under a CC-BY 4.0 license. number of apple pies and pecan pies needs to be summed …

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