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

A goal-oriented meaning-based statistical framework is presented in this paper to solve the math word problem that requires multiple arithmetic operations with understanding, reasoning and explanation. It first analyzes and transforms sentences into their meaning-based logical forms, which represent the associated context of each quantity with role-tags (e.g., nsubj, verb, etc.). Logic forms with role-tags provide a flexible and simple way to specify the physical meaning of a quantity. Afterwards, the main-goal of the problem is decomposed recursively into its associated sub-goals. For each given sub-goal, the associated operator and operands are selected with statistical models. Lastly, it performs inference on logic expressions to get the answer and explains how the answer is obtained in a human comprehensible way. This process thus resembles the human cognitive understanding of the problem and produces a more meaningful problem solving interpretation.