A Novel Approach to Solve Set-Theory Word Problems Automatically

Abstract

Mathematical Word Problems (MWPs) are verbal formulations of real-world scenarios representing an abstract mathematical idea. They aid us in demonstrating the relevance of mathematics in extrapolating everyday tasks. Set Theory is a field of mathematics that is used to discern the nature of sets and the relations between them. Set-theory operations are binary in nature. They are used to depict the type of association between two sets. In the current scenario, the difference in the levels of abstraction of deriving regular expressions and interpreting natural language poses a challenging task. In this paper, we present a novel approach to solve set-theory based word problems automatically using the semantics of the language. Our system analyzes set-theory questions obtained from various sources of informal text that are crowd sourced such as online forums, social media and competitive examination portals and computes the result by discerning the language of the problem. Our algorithm mimics the paradigm through which humans attempt to solve set-theory MWPs. We discretized our approach into two sub-tasks, information extraction and problem solving, implementing separate evaluation for each stage and subsequently ensuring that the error propagation from one phase to the next is curbed and efficiency for each stage can be individually determined. Our system uses language semantics to identify the set entities in a word problem, and subsequently maps these entities in an expression that embodies the problem. In the problem solving phase, we obtain the final result of the word problem by inferring the relation that is to be determined and implementing the corresponding set-theory function to compute the solution. We corroborated our result for the two phases individually using supervised learning. In the information extraction phase, our system exhibited an accuracy of 83.5% and its performance in the problem solving phase is 60%, which though needs improvement but is a good beginning.