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Abstract

Even though ontologies are widely being used to enable interoperability in information-rich endeavours, there is currently no united framework for ontology interoperability itself. Surprisingly little of the state of the art in modularity and structuring, e.g. in software engineering, has been applied to ontology engineering so far. However, application areas like Ambient Assisted Living (AAL), which require synchronization and orchestration of interoperable services, are in dire need of safe and secure ontology interoperability. OntoIOp (Ontology Integration and Interoperability), a new international standard proposed in ISO/TC 37/SC 3, aims at filling this gap.

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Abstract

The Mathematics Subject Classification (MSC), maintained by the American Mathematical Society's Mathematical Reviews (MR) and FIZ Karlsruhe's Zentralblatt für Mathematik (Zbl), is a scheme for classifying publications in mathematics according to their subjects. While it is widely used, its traditional, idiosyncratic conceptualization and representation requires custom implementations of search, query and annotation support. This did not encourage people to create and explore connections of mathematics to subjects of related domains (e.g. science), and it made the scheme hard to maintain. We have reimplemented the current version of MSC2010 as a Linked Open Dataset using SKOS and our focus is concentrated on turning it into the new MSC authority. This paper explains the motivation, and details of our design considerations and how we realized them in the implementation. We present in-the-field use cases and point out how e-science applications can take advantage of the MSC LOD set. We conclude with a roadmap for bootstrapping the presence of mathematical and mathematics-based science, technology, and engineering knowledge on the Web of Data, where it has been noticeably underrepresented so far, starting from MSC/SKOS as a seed.

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Abstract

The Mathematics Subject Classification (MSC), maintained by the American Mathematical Society's Mathematical Reviews (MR) and FIZ Karlsruhe's Zentralblatt für Mathematik (Zbl), is a scheme for classifying publications in mathematics according to their subjects. While it is widely used, its traditional, idiosyncratic conceptualization and representation requires custom implementations of search, query and annotation support. This did not encourage people to create and explore connections of mathematics to subjects of related domains (e.g. science), and it made the scheme hard to maintain. We have reimplemented the current version of MSC2010 as a Linked Open Dataset using SKOS and our focus is concentrated on turning it into the new MSC authority. This paper explains the motivation, and details of our design considerations and how we realized them in the implementation. We present in-the-field use cases and point out how e-science applications can take advantage of the MSC LOD set. We conclude with a roadmap for bootstrapping the presence of mathematical and mathematics-based science, technology, and engineering knowledge on the Web of Data, where it has been noticeably underrepresented so far, starting from MSC/SKOS as a seed.

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Abstract

Mathematics is a ubiquitous foundation of science, technology, and engineering. Specific areas, such as numeric and symbolic computation or logics, enjoy considerable software support. Working mathematicians have recently started to adopt Web 2.0 environment, such as blogs and wikis, but these systems lack machine support for knowledge organization and reuse, and they are disconnected from tools such as computer algebra systems or interactive proof assistants.We argue that such scenarios will benefit from Semantic Web technology. Conversely, mathematics is still underrepresented on the Web of [Linked] Data. There are mathematics-related Linked Data, for example statistical government data or scientific publication databases, but their mathematical semantics has not yet been modeled. We argue that the services for the Web of Data will benefit from a deeper representation of mathematical knowledge. Mathematical knowledge comprises logical and functional structures - formulæ, statements, and theories -, a mixture of rigorous natural language and symbolic notation in documents, application-specific metadata, and discussions about conceptualizations, formalizations, proofs, and (counter-)examples. Our review of approaches to representing these structures covers ontologies for mathematical problems, proofs, interlinked scientific publications, scientific discourse, as well as mathematical metadata vocabularies and domain knowledge from pure and applied mathematics. Many fields of mathematics have not yet been implemented as proper Semantic Web ontologies; however, we show that MathML and OpenMath, the standard XML-based exchange languages for mathematical knowledge, can be fully integrated with RDF representations in order to contribute existing mathematical knowledge to theWeb of Data. We conclude with a roadmap for getting the mathematical Web of Data started: what datasets to publish, how to interlink them, and how to take advantage of these new connections.