Learning to Solve Arithmetic Word Problems with Verb Categorization

Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 523–533, October 25-29, 2014, Doha, Qatar. c⃝2014 Association for Computational Linguistics Learning to Solve Arithmetic Word Problems with Verb Categorization Mohammad Javad Hosseini1, Hannaneh Hajishirzi1, Oren Etzioni2, and Nate Kushman3 1{hosseini, hannaneh}@washington.edu, 2OrenE@allenai.org, 3nkushman@csail.mit.edu 1University of Washington, 2Allen Institute for AI, 3Massachusetts Institute of Technology Abstract This paper presents a novel approach to learning to solve simple arithmetic word problems. Our system, ARIS, analyzes each of the sentences in the problem state- ment to identify the relevant variables and their values. ARIS then maps this infor- mation into an equation that represents the problem, and enables its (trivial) so- lution as shown in Figure 1. The pa- per analyzes the arithmetic-word problems “genre”, identifying seven categories of verbs used in such problems. ARIS learns to categorize verbs with 81.2% accuracy, and is able to solve 77.7% of the problems in a corpus of standard primary school test questions. We report the first learning re- sults on this task without reliance on pre- defined templates and make our data pub- licly available.1 1 Introduction Designing algorithms to automatically solve math and science problems is a long-standing AI chal- lenge (Feigenbaum and Feldman, 1963). For NLP, mathematical word problems are particularly at- tractive because the text is concise and relatively straightforward, while the semantics reduces to simple equations. Arithmetic word problems begin by describing a partial world state, followed by simple updates or elaborations and end with a quantitative ques- tion. For a child, the language understanding part is trivial, but the reasoning may be challenging; for our system, the opposite is true. ARIS needs to 1Our data is available at https://www.cs. washington.edu/nlp/arithmetic. Arithmetic word Problem Liz had 9 black kittens. She gave some of her kittens to Joan. Joan now has 11 kittens. Liz has 5 kittens left and 3 have spots. How many kittens did Joan get? State Transition s1 Liz N: 9 E: Kitten A: Black Liz gave some of her kittens to Joan. s2 Liz N: 9-L1 E: Kitten A: Black Joan N: J0+L1 E: Kitten A: Black give Equation: 9 − x = 5 Solution: x = 4 kittens Figure 1: Example problem and solution. make sense of multiple sentences, as shown in Fig- ure 2, without a priori restrictions on the syntax or vocabulary used to describe the problem. Figure 1 shows an example where ARIS is asked to infer how many kittens Joan received based on facts and constraints expressed in the text, and represented by the state diagram and corresponding equation. While the equation is trivial, the text could have involved assembling toy aircraft, collecting coins, eating cookies, or just about any activity involving changes in the quantities of discrete objects. This paper investigates the task of learning to solve such problems by mapping the verbs in the problem text into categories that describe their im- pact on the world state. While the verbs category is crucial (e.g., what happens …

Content truncated to 500 words