Mathematical Knowledge Acquisition And Implementation Of Mathematical Knowledge Management Platform

With the development of computer and Internet technologies, mathematical platforms and remote teaching systems, more mathematical activities will be based on the Web. It is asserted that the way that people do mathematical activities, including mathematical research, teaching and publishing, will change dramatically in the future. Therefore it is a significant research topic how to establish, manage and use Web-based and content-oriented mathematical repository.NKIMath is a research project started in 2001 at the Knowledge Acquisition and Sharing Group, Institute of Computing Technology, Chinese Academy of Sciences. The objective of this project is to research the theory and methodology of mathematical knowledge acquisition, automated knowledge management, sharing, inference and teaching.The main research tasks of this thesis are as follows:(1) Mathematical knowledge acquisition. Firstly, this thesis introduces the method of mathematical knowledge representation based on ontology, framework, logic and type. In the process of acquiring mathematical knowledge this thesis has improved NKIMath mathematical knowledge representation method. Using mathematical knowledge acquisition method called COKAM, we make an experiment in the mathematical domain including mathematical analysis and abstract algebra to verify the correctness and validity of the representation and acquisition method mentioned in this thesis of mathematical knowledge.(2) Mathematical knowledge syntax checking. In the process of acquiring mathematical knowledge, this thesis analysizes syntax error that will possibly happen in the process of acquiring knowledge and elaborately designs algorithm for syntax checking and implements mathematical knowledge syntax checking tool with development tool of VC6.0 under Windows2000 operating system. Using the syntax checking tool, we have already checked out many syntax errors.(3) Mathematical knowledge semantic checking. This thesis analysizes mathematical knowledge semantic checking, mainly including knowledge redundancy and knowledge inconsistency, and presents elaborate algorithms and data structures for mathematical knowledge semantic checking. This thesis alsotakes compactness into account and presents relevant algorithms and data structures.(4) Expansion to mathematical knowledge management platform. The expansion mainly includes mathematical knowledge acquisition, mathematical knowledge querying and mathematical knowledge syntax checking.