Learning To Use Formulas To Solve Simple Arithmetic Problems

Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics, pages 2144–2153, Berlin, Germany, August 7-12, 2016. c⃝2016 Association for Computational Linguistics Learning To Use Formulas To Solve Simple Arithmetic Problems Arindam Mitra Arizona State University amitra7@asu.edu Chitta Baral Arizona State University chitta@asu.edu Abstract Solving simple arithmetic word problems is one of the challenges in Natural Lan- guage Understanding. This paper presents a novel method to learn to use formulas to solve simple arithmetic word problems. Our system, analyzes each of the sen- tences to identify the variables and their attributes; and automatically maps this in- formation into a higher level representa- tion. It then uses that representation to recognize the presence of a formula along with its associated variables. An equa- tion is then generated from the formal de- scription of the formula. In the training phase, it learns to score the <formula, variables> pair from the systematically generated higher level representation. It is able to solve 86.07% of the problems in a corpus of standard primary school test questions and beats the state-of-the-art by a margin of 8.07%. 1 Introduction Developing algorithms to solve math word prob- lems (Table 1) has been an interest of NLP re- searchers for a long time (Feigenbaum and Feld- man, 1963). It is an interesting topic of study from the point of view of natural language understand- ing and reasoning for several reasons. First, it in- corporates rigorous standards of accurate compre- hension. Second, we know of a good representa- tion to solve the word problems, namely algebraic equations. Finally, the evaluation is straightfor- ward and the problems can be collected easily. In the recent years several challenges have been proposed for natural language understanding. This includes the Winograd Schema challenge for commonsense reasoning (Levesque, 2011), Story Comprehension Challenge (Richardson et al., 2013), Facebook bAbl task (Weston et al., 2015), Semantic Textual Similarity (Agirre et al., 2012) and Textual Entailment (Bowman et al., 2015; Dagan et al., 2010). The study of word math problems is also an important problem as quantita- tive reasoning is inextricably related to human life. Clark & Etzioni (Clark, 2015; Clark and Etzioni, 2016) discuss various properties of math word (and science) problems emphasizing elementary school science and math tests as a driver for AI. Researchers at Allen AI Institute have published two standard datasets as part of the Project Euclid1 for future endeavors in this regard. One of them contains simple addition-subtraction arithmetic problems (Hosseini et al., 2014) and the other contains general arithmetic problems (Koncel- Kedziorski et al., 2015). In this research, we focus on the former one, namely the AddSub dataset. Dan grew 42 turnips and 38 cantelopes . Jes- sica grew 47 turnips . How many turnips did they grow in total ? Formula Associated variables part-whole whole: x, parts: {42, 47} Equation x = 42 + 47 Table 1: Solving a word problem using part-whole Broadly speaking, common to the existing ap- proaches (Kushman et al., 2014; Hosseini et al., 2014; …

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