Designing a Tag-Based Statistical Math Word Problem Solver with Reasoning and Explanation

Abstract: Background Since Big Data mainly aims to explore the correlation between surface features but not their underlying causality relationship, the Big Mechanism 2 program has been proposed by DARPA to find out “why” behind the “Big Data”. However, the pre-requisite for it is that the machine can read each document and learn its associated knowledge, which is the task of Machine Reading (MR). Since a domain-independent MR system is complicated and difficult to build, the math word problem (MWP) [1] is frequently chosen as the first test case to study MR (as it usually uses less complicated syntax and requires less amount of domain knowledge). According to the framework for making the decision while there are several candidates, previous MWP algebra solvers can be classified into: (1) Rule-based approaches with logic inference [2-7], which apply rules to get the answer (via identifying entities, quantities, operations, etc.) with a logic inference engine. (2) Rule-based approaches without logic inference [8-13], which apply rules to get the answer without a logic inference engine. (3) Statistics-based approaches [14, 15], which use statistical models to identify entities, quantities, operations, and get the answer. To our knowledge, all the statistics-based approaches do not adopt logic inference. The main problem of the rule-based approaches mentioned above is that the coverage rate problem is serious, as rules with wide coverage are difficult and expensive to construct. Also, since they adopt Go/No-Go approach (unlike statistical approaches which can adopt a large Top-N to have high including rates), the error accumulation problem would be severe. On the other hand, the main problem of those approaches without adopting logic inference is that they usually need to implement a new handling procedure for each new type of problems (as the general logic inference mechanism is not adopted). Also, as there is no inference engine to generate the reasoning chain [16], additional effort would be required for