Reasoning about Quantities in Natural Language

Reasoning about Quantities in Natural Language Subhro Roy University of Illinois, Urbana Champaign sroy9@illinois.edu Tim Vieira Johns Hopkins University tim.f.vieira@gmail.com Dan Roth University of Illinois, Urbana Champaign danr@illinois.edu Abstract Little work from the Natural Language Processing community has targeted the role of quantities in Natural Language Understanding. This paper takes some key steps towards facilitating reasoning about quantities expressed in natural language. We investigate two different tasks of numerical reasoning. First, we consider toQuantity Entailment, a new task formulated understand the role of quantities in general textual inference tasks. Second, we consider the problem of automatically understanding and solving elementary school math word problems. In order to address these quantitative reasoning problems we first develop a computational approach which we show to successfully recognize and normalize textual expressions of quantities. We then use these capabilities to further develop algorithms to assist reasoning in the context of the aforementioned tasks. 1 Introduction Every day, newspaper articles report statistics to present an objective assessment of the situations they describe. From election results, number of casualties in accidents, to changes in stock prices, textual representations of quantities are extremely important in communicating accurate information. However, relatively little work in Natural Language Processing has analyzed the use of quantities in text. Even in areas where we have relatively mature solutions, like search, we fail to deal with quantities; for example, one cannot search the financial media for “transactions in the 1-2 million pounds range.” Language understanding often requires the ability to reason with respect to quantities. Consider, for example, the following textual inference, which we present as Textual Entailment query. Recognizing Textual Entailment (RTE) (Dagan et al., 2013) has become a common way to formulate textual inference and we follow this trend. RTE is the task of determining whether the meaning of a given text passage T entails that of a hypothesis H. Example 1 T:A bomb in a Hebrew University cafeteria killed five Americans and four Israelis. H:A bombing at Hebrew University in Jerusalem killed nine people, including five Americans. Here, we need to identify the quantities “five Americans” and “four Israelis”, as well as use the fact that “Americans” and “Israelis” are “people”. A different flavour of numeric reasoning is required in math word problems. For example, in Example 2 Ryan has 72 marbles and 17 blocks. If he shares the marbles among 9 friends, how many marbles does each friend get? one has to determine the relevant quantities in the question. Here, the number of blocks in Ryan’s possession has no bearing on the answer. The second challenge is to determine the relevant mathematical operation from the context. In this paper, we describe some key steps necessary to facilitate reasoning about quantities in natural language text. We first describe a system developed to recognize quantities in free form text, infer units associated with them and convert them to 1 Transactions of the Association for Computational Linguistics, vol. 3, pp. 1–13, 2015. Action Editors: Johan Bos, Lillian Lee. Submission batch: 6/2014; Revision …

Content truncated to 500 words