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.

翻译：本文致力于基于本体的数学知识管理与表示问题。主要关注点在开放关联数据云中数学陈述表示的形式模型开发。所提出的模型适用于从自然语言数学文本中提取数学事实并将这些事实表示为关联开放数据的应用场景。该模型被用于描述专业数学本体OntoMath${}^{\mathrm{PRO}}$新版本的开发过程。OntoMath${}^{\mathrm{PRO}}$支撑着一个语义出版平台，该平台以LaTeX格式的数学论文集合为输入，构建其基于本体的关联开放数据表示。该语义出版平台进而成为OntoMath数字生态系统的核心组件——一个融合本体、文本分析工具及数学知识管理应用的生态系统，涵盖数学公式的语义搜索与数学论文推荐系统。根据新模型，该本体被组织为三个层次：基础本体层、领域本体层和语言层。领域本体层包含与语言无关的数学概念。语言层为这些概念提供语言基础，基础本体层则为它们提供元本体注释。这些概念按照两大层级结构进行组织：对象层级与物化关系层级。