A new version of the ontology of professional mathematical knowledge OntoMathPRO is presented. This ontology is a conceptual model of the main branches of mathematics. The new version of the ontology introduces materialized relationships between concepts. To do this, ontology concepts are additionally divided into types and roles. Concepts-roles act as arguments of materialized relations. 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.

conceptual model of mathematics, mathematical ontology, OntoMathPRO ontology, materialized relation, subject ontology, representation of mathematical knowledge

Elizarov Aleksandr Mikhajlovich,  ,  orcid.org/0000-0003-2546-6897,  Institute of Information Technologies and Intelligent Systems of Kazan Federal University; N. I. Lobachevskii Institute of Mathematics and Mechanics KFU; Joint Supercomputer Center of the Russian Academy of Sciences in Kazan

Kirillovich Alexander Vitalevich,  ,  orcid.org/0000-0001-9680-449X,  Joint Supercomputer Center of the Russian Academy of Sciences in Kazan

Lipachev Evgeny Konstantinovich,  ,  orcid.org/0000-0001-7789-2332,  Institute of Information Technologies and Intelligent Systems of Kazan Federal University; N. I. Lobachevskii Institute of Mathematics and Mechanics KFU

Nevzoova Olga Avenirovna,  ,  orcid.org/0000-0001-8116-9446,  Kazan Federal University