Abstract:

Developing and using domain ontologies is a part of the project directed on creating a single large space of scientific knowledge. The using domain ontologies contributes to solving the important problem of building recommender systems as components of information platforms for decision support system. The using ontologies in teaching educational systems, in particular, to control mathematical knowledge, is another important goal of building mathematical ontologies. The importance of projects on the application of semantic technologies in mathematics in accordance with the principles of Linked Open Data (LOD, https://lod-cloud.net/) has been noted in various studies.
Today, on the basis of OntoMathPRO ontology, semantic services for managing mathematical knowledge have already been designed. These services are included in the OntoMath digital ecosystem, within which software tools for the formation of electronic mathematical collections are developed. We also note that the first version of the ontology of professional mathematical knowledge OntoMathPRO has applied in projects for designing other domain ontologies, building platforms for scientific search and systems for assessing the quality of knowledge.
The implemented practical applications of the OntoMathPRO ontology revealed a number of limitations of its existing version and made it possible to formulate goals for further development. In the new version of the ontology, a number of modern fields of mathematics are formalized, new types of relationships between concepts are introduced, such as prerequisites, which are necessary to create educational services.
The sections "Ordinary differential equations" and "Partial differential equations" are formalized. This allows using this knowledge base for educational purposes.
Also, one of the features of the new version of the ontology is the inclusion of multilingual lexicons for expressing mathematical concepts in natural language texts. The introduction of prerequisite relationships between ontology classes has expanded the possibilities of creating educational mathematical applications. Some important applications of the OntoMathPRO ontology in various fields of knowledge are indicated.
The developed software tools make it possible to design new intelligent services for managing mathematical knowledge and form a single digital space of mathematical knowledge based on extended representation formalisms.

Keywords:

Mathematical knowledge, ontology, prerequisite, educational system.