Quantitative reasoning involves understanding the use of quantities and numeric relations in text, and reasoning with respect to them. It forms an essential part of everyday interaction. However, little work from the Natural Language Processing community has focused on quantitative reasoning. In this thesis, we investigate the challenges in performing automated quantitative reasoning over natural language text. We formulate several tasks to tackle some of the fundamental problems of quantitative reasoning, and address the problem of developing robust statistical methods for these tasks.
We show that standard NLP tools are not sufficient to obtain the abstraction needed for quantitative reasoning; the standard NLP pipeline needs to be extended in various ways. We propose several technical ideas for these extensions. We first look at the problem of detecting and normalizing quantities expressed in free form text, and show that correct detection and normalization can support several simple quantitative inferences. We then focus on numeric relation extraction from sentences, and show that several natural properties of language can be leveraged to effectively extract numeric relations from a sentence.
We finally investigate the problem of quantitative reasoning over multiple quantities mentioned across several sentences. We develop a decomposition strategy which allows reasoning over pairs of numbers to be combined effectively to perform global reasoning. We also look at the problem of effectively using math domain knowledge in quantitative reasoning. On this front, we first propose graph representations called "unit dependency graphs'', and show that these graph representations can be used to effectively incorporate dimensional analysis knowledge in quantitative reasoning. Next, we develop a general framework to incorporate any declarative knowledge into quantitative reasoning. This framework is used to incorporate several mathematical concepts into textual quantitative reasoning, leading to robust reasoning systems
