Solving arithmetic word problems by synergizing syntax-semantics extractor for explicit relations and neural network miner for implicit relations

Abstract

Abstract This paper presents a relation-centric algorithm for solving arithmetic word problems (AWPs) by synergizing a syntax-semantics extractor for extracting explicit relations, and a neural network miner for mining implicit relations. This is the first algorithm that has a specific component to acquire implicit knowledge items for solving AWPs. This paper proposes a three-phase scheme to decompose the challenging task of designing an algorithm for solving AWPs into three smaller tasks. The first phase proposes a state-action paradigm; the second phase instantiates the paradigm into a relation-centric approach; and the third phase implements a relation-centric algorithm for solving AWPs. There are two main steps in the proposed algorithm: problem understanding and symbolic solver. By adopting the relation-centric approach, problem understanding becomes a task of relation acquisition. For conducting the task of relation acquisition, a relaxed syntax-semantics method first extracts a group of explicit relation candidates. In parallel, a neural network miner acquires implicit relation candidates. The miner computes the vectors encoded by BERT to determine which implicit relations should be added. Thus, problem understanding can acquire both explicit relations and implicit relations, which addresses the challenge of building a problem understanding method that can acquire all the knowledge items to find the solution. In the subsequent step of symbolic solver, a fusion procedure forms a distilled set of relations from all the candidates by discarding unnecessary relations. Experimentation on nine benchmark datasets validates the superiority of the proposed algorithm that outperforms the state-of-the-art algorithms.

Keywords

• Problem solving
• State-action paradigm
• Relation-centric
• Explicit relation
• Implicit relation
• Syntax-semantics model