OLGA : An Ontology and LSTM-based approach for generating Arithmetic Word Problems of transfer type

Machine generation of Arithmetic Word Problems (AWPs) is challenging as they express quantities and mathematical relationships and need to be consistent. ML-solvers require a large annotated training set of consistent problems with language variations. Exploiting domain-knowledge is needed for consistency checking whereas LSTM-based approaches are good for producing text with language variations. Combining these we propose a system, OLGA, to generate consistent word problems of TC (Transfer-Case) type, involving object transfers among agents. Though we provide a dataset of consistent 2-agent TC-problems for training, only about 36% of the outputs of an LSTM-based generator are found consistent. We use an extension of TC-Ontology, proposed by us previously, to determine the consistency of problems. Among the remaining 64%, about 40% have minor errors which we repair using the same ontology. To check consistency and for the repair process, we construct an instance-specific representation (ABox) of an auto-generated problem. We use a sentence classifier and BERT models for this task. The training set for these LMs is problem-texts where sentence-parts are annotated with ontology class-names. As three-agent problems are longer, the percentage of consistent problems generated by an LSTM-based approach drops further. Hence, we propose an ontology-based method that extends consistent 2-agent problems into consistent 3-agent problems. Overall, our approach generates a large number of consistent TC-type AWPs involving 2 or 3 agents. As ABox has all the information of a problem, any annotations can also be generated. Adopting the proposed approach to generate other types of AWPs is interesting future work.