  This paper is devoted to the problems of ontology-based mathematical
knowledge management and representation. The main attention is paid to the
development of a formal model for the representation of mathematical statements
in the Open Linked Data cloud. The proposed model is intended for applications
that extract mathematical facts from natural language mathematical texts and
represent these facts as Linked Open Data. The model is used in development of
a new version of the OntoMath${}^{\mathrm{PRO}}$ ontology of professional
mathematics is described. OntoMath${}^{\mathrm{PRO}}$ underlies a semantic
publishing platform, that takes as an input a collection of mathematical papers
in LaTeX format and builds their ontology-based Linked Open Data
representation. The semantic publishing platform, in turn, is a central
component of OntoMath digital ecosystem, an ecosystem of ontologies, text
analytics tools, and applications for mathematical knowledge management,
including semantic search for mathematical formulas and a recommender system
for mathematical papers. According to the new model, the ontology is organized
into three layers: a foundational ontology layer, a domain ontology layer and a
linguistic layer. The domain ontology layer contains language-independent math
concepts. The linguistic layer provides linguistic grounding for these
concepts, and the foundation ontology layer provides them with meta-ontological
annotations. The concepts are organized in two main hierarchies: the hierarchy
of objects and the hierarchy of reified relationships.
