A Tag-based English Math Word Problem Solver with Understanding, Reasoning and Explanation

Abstract

This paper presents a tag-based statistical math word problem solver with understanding, reasoning, and explanation. It analyzes the text and transforms both body and question parts into their tag-based logic forms, and then performs inference on them. The proposed tag-based approach provides the flexibility for annotating an extracted math quantity with its associated syntactic and semantic information, which can be used to identify the desired operand and filter out irrelevant quantities. The proposed approach is thus less sensitive to the irrelevant information and could provide the answer more precisely. Also, it can handle much more problem types other than addition and subtraction.

A Goal-Oriented Meaning-based Statistical Multi-Step Math Word Problem Solver with Understanding, Reasoning and Explanation

“…The Logic Form Converter (LFC) then transforms the linguistic representation into logic forms and constructs the final operation tree. Besides, the LFC also calls the Solution Type Classifier (STC) to determine the solution type and calls the Inference Engine (IE) [Liang et al, 2016] to evaluate the given operation tree and generate the answer for the question. Lastly, the Explanation Generator (EG) [Huang et al, 2015] generates the explanation text to explain how the answer is obtained according to the given reasoning chain.…”

“…Lastly, the Explanation Generator (EG) [Huang et al, 2015] generates the explanation text to explain how the answer is obtained according to the given reasoning chain. We adopt the same STC, IE and EG modules used in [Liang et al, 2016], and only describe new modules below.…”

“…The LFC transforms each quantity into its first-order logic form [Lin et al, 2015;Russell and Norvig, 2009]. All quantities and the main-goal are first identified by rules and explicitly associated with their role-tags, which carries context information and specifies the physical meaning of that quantity.…”

“…The math word problem (MWP) was frequently chosen to study the task of natural language understanding and simulate human problem solving procedure [Bakman, 2007;Liang et al, 2016]. However, many previous approaches either only handled MWPs that involve one arithmetic operation [Mukherjee and Garain, 2008; or solved multi-step arithmetic operations with various limitations (e.g., only handling Addition and Subtraction sequence [Ma et al, 2010;Hosseini et al, 2014;Mitra and Baral, 2016]).…”

Giving BERT a Calculator: Finding Operations and Arguments with Reading Comprehension

“…Instead, the main challenge is mathematical reasoning. According toZhang et al (2018), the current state of the art uses syntactic parses and deterministic rules to convert the input to logical forms(Liang et al, 2016).…”