Towards a mathematical knowledge management system: Ontology to model linear equations

Abstract

Knowledge management systems based on ontologies are an important software tool to maintain the knowledge of experts, however, the mathematical area needs to improve aspects such as creating repositories of formalized mathematics, mathematical search and retrieval, and implementing math assistants. This article proposes an ontology to be used in a Mathematical Knowledge Management System (MKMS) with the objective of storing and retrieving systems of linear equations, these equations will serve to teach students to solve problems with an approach based on examples. We built the ontology considering following phases: specification, conceptualization, formalization, and implementation. Besides, the ontology was evaluated before incorporating it into the MKMS. Finally, the article shows a general architecture of the MKMS to understand the theoretical operation. Although ontology focuses on modeling a single topic, it defines the basis for modeling other mathematics topics and being applied in an MKMS.