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.

Word annotation has been adopted as a crucial preprocessing step in developing algorithms for solving arithmetic word problems (AWPs). This paper proposes a mathematical concepts enhanced annotation (MONA) model for Chinese arithmetic word problems (AWPs), consisting of two modules: mathematical Chinese word segmentation and mathematical part-of-speech tagging. The MONA model utilizes mathematical concepts to enhance the training tasks of both modules, improving their capabilities to ensure high-quality AWPs annotations. The mathematical Chinese word segmentation module is trained on an AWP corpus segmented based on mathematical concepts, resulting in higher accuracy in identifying mathematical concepts compared to general segmentation models. The mathematical part-of-speech tagging module redefines part-of-speech categories into seven classes according to mathematical concepts and trains the MONA model on the redefined part-of-speech tags, allowing more suitable part-of-speech tagging for acquiring math relations when solving AWPs. Experimental results show the proposed MONA model outperforms baseline models on benchmark AWP datasets.

Automatic solutions to Arithmetic Word Problems (AWPs) continue to attract significant attention due to their potential uses in fact-checking, validation as well as problem-solving across science, industry, and education. For the latter field specifically, there is significant untapped potential from the automation of AWPs for the full integration of intelligent tutors into educational processes, being the focus of this work. To aid the demystification of AWP, a range of algorithms has been proposed in recent years with some of these documenting incremental increases in accuracy. Some, however, are not suitable for broad application as they cannot generate readable solutions required for intelligent tutoring. This work aims to increase the accuracy of explicit AWP solutions, bring transparency to the AWP problem-solving process, and generate intermediate readable solutions by proposing a hybrid algorithm that combines superior features from existing methods with “Ongraph” Vector Computing. The essential creativity lies in that the proposed Ongraph vector computing fuses the bests of graph and vector computing and that it integrates the vector syntax-semantics method. Experimental results obtained from the test on six authoritative datasets confirm that the proposed algorithm improves accuracy for automated solutions of AWPs thus making a significant contribution to the body of work on AWP-based problem-solving.