OntoMath$^{\operatorname{PRO}}$ : An ontology of mathematical knowledge

The article describes OntoMath$^{\operatorname{PRO}}$, the first Linked Open Data ontology of professional mathematical knowledge. The ontology is designed to represent mathematical concepts. The concepts of the ontology are organized into two hierarchies: a hierarchy of mathematical objects and a hierarchy of reified relationships. OntoMath$^{\operatorname{PRO}}$ respects meta-ontological distinctions provided by a foundational ontology and annotates the concepts as kinds and roles. Relationships between mathematical objects are represented in a reified form, i.e., as instances of relationship concepts linked to their arguments that are instances of role concepts. The ontology defines multilingual lexicons that describe how the concepts are expressed in natural language text. The lexicons are represented as Linguistic Linked Open Data datasets. The OntoMath$^{\operatorname{PRO}}$ ontology is under development and will be enriched by new areas of mathematics.