Christoph Lange

• The aim of the research presented in this technical report was, and still is, to develop a wiki (Leuf and Cunningham, 2001) technology for collaboratively building, editing and browsing mathematical knowledge. This technology is being prototyped in the SWiM system (S-emantic Wi-ki for M-athematical Knowledge Management). Its hyperlinked pages, containing mathematical theories and statements, are stored in OMDoc (Kohlhase, 2006), a markup format for mathematical knowledge representation with numerous applications: creation of customized modules for e-learning, data exchange between different theorem provers, web services and more. SWiM has been intended to be based on an already existing wiki software, preferably a semantic one. SWiM will encourage users to collaborate: non-mathematicians can collaborate in creating a "Wikipedia (Wikipedia, 2006) of mathematics" by compiling the knowledge available so far, while scientists can collaboratively develop new theories. However, to encourage users to contribute, wiki-like openness to anybody probably will not suffice. Unlike the text formats used by common semantic wikis, the OMDoc format makes the fine-grained semantic structure that is implicit in the text explicit in the markup, making it tedious to author by hand. Moreover, only after a substantial initial investment (writing, annotating and linking) on the author's part, the community can benefit from the added-value services supported by the format - e.g. the creation of customized textbooks (Melis and Siekmann, 2004). If author and beneficiary of such services were different persons, though, only few persons would be willing to contribute to a knowledge base. This "MKM 2 author’s dilemma" (Kohlhase and Kohlhase, 2004) can be overcome when the authors themselves are rewarded for their contributions by being offered added-value services, which improve as soon as users contribute annotations and cross-references, - for example a facility for navigation through the knowledge base along paths of semantic relations between the theories, which are computed from the OMDoc document collection. The contribution of this research is threefold: 1. The architecture of SWiM has been specified. 2. A partial implementation has been done, and it has been evaluated. 3. Parts of the OMDoc 1.2 standard have been improved (mainly those parts used in the SWiM implementation, i.e. the example documents, the presen- tation XSLT style sheets and the system ontology). Further information about the project is available from its homepage http://kwarc.eecs.iu-bremen.de/projects/swim/ . A ready-to-install package will be available for download there from March 2007, and an online demo is available. The research presented here has been conducted from February to August 2006 in the context of my diploma thesis, which has been supervised by Prof. Bernd Walter (University of Trier) and Prof. Michael Kohlhase (Jacobs University Bremen) (Lange, 2006a). For this report, the thesis has been revised. Outdated facts have been brought up-to-date, and certain aspects of the evaluation have been concretized with further research on this topic for my Ph.D. thesis in mind, but the requirements analysis (section 2), the specification (section 3) and the implementation described in section 4 remained unchanged.