Mathematics is becoming increasingly collaborative, but software does not sufficiently support that: Social Web applications do not currently make mathematical knowledge accessible to automated agents that have a deeper understanding of mathematical structures. Such agents exist but focus on individual research tasks, such as authoring, publishing, peer-review, or verification, instead of complex collaboration workflows.
This work effectively enables their integration by bridging the document-oriented perspective of mathematical authoring and publishing, and the network perspective of threaded discussions and Web information retrieval. This is achieved by giving existing representations of mathematical and relevant related knowledge about applications, projects and people a common Semantic Web foundation. Service integration is addressed from the two perspectives of enriching published documents by embedding assistive services, and translating between different knowledge representations inside knowledge bases. A usability evaluation of a semantic wiki that coherently integrates knowledge production and consumption services points out the remaining challenges in making such heterogeneously integrated environments support realistic workflows.
The results of this thesis will soon also enable collaborative acquisition of new mathematical knowledge, as well as the contributions of existing knowledge collections of the Web of Data.
This thesis presents a collection of methods and technologies that enable building a collaboration infrastructure for managing mathematical knowledge in a way that makes it comprehensible, reusable, and applicable. Working mathematicians have already embraced Social Web applications such as blogs for communication and collaboration, but these neither make knowledge accessible to automated agents for, e.g., verification or computation, nor to specific audiences such as students having less background knowledge than the original authors. The key challenge addressed in this thesis is effectively supporting collaborative mathematical knowledge management (MKM) workflows by making the knowledge comprehensible to a wide range of services, while aiming at an entry barrier that, for a domain expert, is not disproportionately higher than that of successful Social Web sites.
As the building blocks for the envisaged collaboration environment were not available in a way that would merely have required putting them together, the main focus of this thesis is “under the hood”, i.e. in preparing these building blocks. To get an idea of the building blocks, consider the workflow of writing a research paper: That involves formalizing the original idea from one's mind into a structured document, searching existing knowledge to build on, validating the formal structure, presenting the content in a comprehensible way, and submitting it for review. Reviewers would look up background information in cited publications, and point out problems with the paper and the formal concepts it introduces. Previous research on MKM has produced services that effectively support the primitive tasks that the overall workflow is composed of. However, these services take different perspectives on mathematical knowledge and speak different languages, which restricts their integration.
Our integration approach starts with opening up a wider audience for existing expressive mathematical knowledge representation languages – in the first step an “audience” of machines, which then make the mathematical knowledge accessible to their human end users. We improve the interoperability of different mathematical knowledge representations with each other, and with sources of non-mathematical knowledge about applications, projects, and people, by putting them on a common Semantic Web foundation that combines the document-oriented view of mathematical authoring and publishing with the network-oriented view of the growing Web of Data and Web-based information retrieval.
We address service integration from two perspectives: enriching published documents by embedding assistive services, and integrating translations between different knowledge representations transparently into a knowledge base. Ultimately, we combine both perspectives into a semantic wiki environment for collaboratively producing and consuming mathematical knowledge. This serves as a prototype for evaluating the effectivity of supporting realistic workflows following our integration approach. An evaluation of the wiki's usability in the setting of maintaining a widely used collection of semiformal mathematical knowledge helps to understand the remaining challenges in making environments that integrate heterogeneous services for different knowledge representations learnable, effective, useful, and satisfying to use.
Finally, we discuss future directions in combining the building blocks obtained in this work towards e-science on the Web: supporting scientists in collaboratively gaining new knowledge, and steps towards contributing existing collections of mathematical knowledge to the Web of Data.
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