Solving General Arithmetic Word Problems

Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pages 1743–1752, Lisbon, Portugal, 17-21 September 2015. c⃝2015 Association for Computational Linguistics. Solving General Arithmetic Word Problems Subhro Roy University of Illinois, Urbana Champaign sroy9@illinois.edu Dan Roth University of Illinois, Urbana Champaign danr@illinois.edu Abstract This paper presents a novel approach to au- tomatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multi- ple steps and operations, without depending on additional annotations or predefined tem- plates. We develop a theory for expression trees that can be used to represent and evalu- ate the target arithmetic expressions; we use it to uniquely decompose the target arithmetic problem to multiple classification problems; we then compose an expression tree, combin- ing these with world knowledge through a con- strained inference framework. Our classifiers gain from the use of quantity schemas that sup- ports better extraction of features. Experimen- tal results show that our method outperforms existing systems, achieving state of the art per- formance on benchmark datasets of arithmetic word problems. 1 Introduction In recent years there is growing interest in understand- ing natural language text for the purpose of answering science related questions from text as well as quanti- tative problems of various kinds. In this context, un- derstanding and solving arithmetic word problems is of specific interest. Word problems arise naturally when reading the financial section of a newspaper, following election coverage, or when studying elementary school arithmetic word problems. These problems pose an in- teresting challenge to the NLP community, due to its concise and relatively straightforward text, and seem- ingly simple semantics. Arithmetic word problems are usually directed towards elementary school students, and can be solved by combining the numbers men- tioned in text with basic operations (addition, subtrac- tion, multiplication, division). They are simpler than algebra word problems which require students to iden- tify variables, and form equations with these variables to solve the problem. Initial methods to address arithmetic word problems have mostly focussed on subsets of problems, restrict- ing the number or the type of operations used (Roy et al., 2015; Hosseini et al., 2014) but could not deal with multi-step arithmetic problems involving all four basic operations. The template based method of (Kushman et al., 2014), on the other hand, can deal with all types of problems, but implicitly assumes that the solution is generated from a set of predefined equation templates. In this paper, we present a novel approach which can solve a general class of arithmetic problems with- out predefined equation templates. In particular, it can handle multiple step arithmetic problems as shown in Example 1. Example 1 Gwen was organizing her book case making sure each of the shelves had exactly 9 books on it. She has 2 types of books - mystery books and picture books. If she had 3 shelves of mystery books and 5 shelves of picture books, how many books did she have in total? The solution involves understanding …

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