Abstract:

The article provides an overview of existing digital publishing systems, existing ways to expand the functionality of such systems, and also proposes a project for a set of services to expand the functionality of the Open Journal Systems publishing system on the platform of the Lobachevskii-DML digital mathematical library. The proposed set of services includes services aimed at the authors of articles and intended for the editorial staff of the journal. The existing developments in individual parts of the project are described, and the main ideas for the development of all services are proposed.

Abstract:

We present a set of semantic services developed by us to support the educational process in mathematics. The functionality of these services is based on the use of mathematical ontologies OntoMath^Edu and OntoMath^PRO. The ontology of professional mathematical knowledge OntoMath^PRO is designed to classify and systematize the concepts of professional mathematics and includes several important areas of mathematics. Educational mathematical ontology OntoMath^Edu systematically represents knowledge on the training course “Planimetry”. For the use of ontologies in educational applications, an approach to the design of prerequisite relations in these ontologies has been developed. To support mathematical education, we have developed: a service for semantic search by mathematical formulas, a service for semantic annotation of educational materials, a service for visualizing subgraphs of the OntoMath^Edu ontology semantic network, a parallel formal/informal corpus of mathematical statements, a system for automatically generating test questions in mathematical disciplines.

We provide examples of successful application of the developed software tools.

The created software tools are built into the OntoMath digital ecosystem. This ecosystem implements the interaction of semantic services for managing mathematical knowledge.

Abstract:

Classification of documents with the assignment of classifier codes is a traditional way of systematizing and searching for documents on a specific topic. The Universal Decimal Classification (UDC) underlies the systematization of knowledge presented in libraries, databases and other information repositories. In Russia, UDC is an obligatory attribute of all book production and information on natural and technical sciences. The choice of classification codes is associated with the analysis of the structure of the classifier tree and is traditionally decided by the author of a scientific article. This article proposes a solution for automating the assigning the UDC classification code for a mathematical article based on a special resource – the OntoMath^PRO ontology for professional mathematics, developed at Kazan Federal University. An approach to solving the problem is to create "code maps" for each classifying code in the UDC tree in the field of mathematics. Under the "code map" is meant a weighted set of all extracted, with the help of OntoMath^PRO ontology, mathematical named entities from the collection of articles with a given UDC code. The creation of "code maps" is based on the hypothesis that the choice of the UDC code is determined by a certain set of classifying features that can be represented by classes from the OntoMath^PRO ontology. The proposed hypothesis was tested and confirmed in the paper. The hypothesis was tested on a collection of mathematical articles An approach to solving the problem is to create "code maps" for each classifying code in the UDC tree in the field of mathematics. Under the "code map" is meant a weighted set of all extracted, with the help of OntoMath^PRO ontology, mathematical named entities from the collection of articles with a given UDC code. The creation of "code maps" is based on the hypothesis that the choice of the UDC code is determined by a certain set of classifying features that can be represented by classes from the OntoMath^PRO ontology. The proposed hypothesis was tested and confirmed in the paper.  The hypothesis was tested on a collection of mathematical articles published during 1999-2009 in the "Izvestiya VUZov. Mathematics" journal. 

Abstract:

The results on the creation of methods for managing mathematical knowledge in the context of digital mathematical libraries are presented. The software tools developed on the basis of these methods are part of the OntoMath digital ecosystem, within which they interact. A brief description of the architecture of the OntoMath ecosystem is given, the levels of subject ontologies and external ontologies are highlighted, as well as the level of software tools and services. Semantic services are separated into a separate category. This term denotes software tools, in the functionality of which queries to subject ontologies are used to ensure the management of knowledge objects. General descriptions of developed subject ontologies are given: educational mathematical ontology OntoMath^Edu and ontology of professional mathematics OntoMath^PRO. The development of educational ontology is reflected in the direction of including educational prerequisite links between classes. Among the software tools of the digital ecosystem, search services for mathematical electronic collections, a service for semantic annotation of mathematical documents, tools for semantic marking of educational mathematical documents, as well as a system for automatically generating testing tests in mathematical educational disciplines are highlighted. As part of the OntoMath digital ecosystem, special-purpose recommender systems are being developed. The current version of the ecosystem includes a recommender system for generating a list of related articles based on the OntoMath^PRO ontology, a recommender system for appointing experts to support the scientific review process, and recommender systems for selecting subject classifiers UDC and Mathematics Subject Classification codes for mathematical documents. The results are also presented in the direction of creating a digital library metadata factory, which includes services and tools for extracting, refining, replenishing and normalizing the metadata of electronic mathematical collections. Note that the OntoMath ecosystem is being developed as the technological basis for the Lobachevskii Digital Mathematical Library.

Abstract: This review discusses methods and algorithms for increasing linked data expressiveness which are prepared for Web publication. The main approaches to the enrichment of ontologies are considered, the methods on which they are based and the tools for implementing the corresponding methods are described.The main stage in the general scheme of the related data life cycle in a cloud of Linked Open Data is the stage of building a set of related RDF- triples. To improve the classification of data and the analysis of their quality, various methods are used to increase the expressiveness of related data. The main ideas of these methods are concerned with the enrichment of existing ontologies (an expansion of the basic scheme of knowledge) by adding or improving terminological axioms. Enrichment methods are based on methods used in various fields, such as knowledge representation, machine learning, statistics, natural language processing, analysis of formal concepts, and game theory.

Abstract:

This article provides an overview of existing solutions for semantic analysis of mathematical documents, and also presents a method for automatic semantic analysis of documents in PDF format. This method searches for local variables in the text of the article, extracts their definitions and connects concepts with formulas. The advantage of the method over the existing ones is independence from the markup of the original PDF document, which expands the scope of the method. We provide estimates of recall, precision and F-measure for algorithms for finding variables and linking local variables with formulas. The resulting semantic markup of the document will be used to create a collection of documents suitable for the semantic formula search service, which is part of the set of services of the Lobachevskii-DML digital publishing system.