Description
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.
Chapter
Structure and Contribution of this Thesis
Part II. Knowledge Representation
Chapter 2. Representing Mathematical Knowledge
Structures of Mathematical Knowledge
Requirements for Reusably Representing and Exchanging Mathematical Knowledge
Knowledge Representation on the [Semantic] Web (State of the Art)
Representing Semiformal Mathematical Knowledge (State of the Art)
Designing an Improved Representation and Exchange Language
Chapter 3. Ontologies for Structures of Mathematical Knowledge
Overview of the Ontologies by Structural Dimension
Logical and Functional Structures, and Notation
Rhetorical and Document Structures
The Application Environment
Discussions about Knowledge Items
Requirements for Extracting Structures from Semantic Markup to RDF
Conclusion and Future Work
Chapter 4. Using Mathematical Markup for Implementing and Documenting Expressive Ontologies
Problem and Requirements Statement
Implementing and Documenting Heterogeneous Ontologies in OMDoc
Implementation of the OMDoc Ontology
Case Study: Reimplementing FOAF in OMDoc
Conclusion and Future Work
Chapter 5. Multi-Dimensional Metadata Markup
The Metadata Syntax of OMDoc 1.2 (State of the Art)
The new OMDoc+RDFa Metadata Framework
Part III. Services and their Integration
Chapter 6. Primitive Services for Managing Mathematical Knowledge
Tasks, Scenarios, and Required Primitive Services
Human- and Machine-Comprehensible Publishing
Arguing about Problems and their Solutions
Chapter 7. Integrating Assistive Services into Interactive Documents
State of the Art and Related Work
Requirements for Integrating Services into Documents
In-Document Client Services
Symbol-based Client Services
Expression-based Client Services
Conclusion and Future Work
Chapter 8. Transparent Translations in Knowledge Bases
Extracting Structures from Semantic Markup
Migration to More Expressive Languages
Coping with Different Representation Granularities on Import and Export
Recommendations for Running Translations Transparently
Chapter 9. The Semantic Wiki SWiM - An Integrated Collaboration Environment
Wikis and Semantic Wikis (State of the Art)
Requirements Analysis and Design Decisions
How SWiM Supports OpenMath CD Maintenance Workflows
Conclusion and Future Work
Chapter 10. Usability Evaluation of an Integrated Environment for Maintaining Semiformal Collections
Evaluation Hypotheses and Method
Quantitative Content Analysis of Argumentative Discussions
Supervised Usability Experiments with Test Users
Evaluation Results and their Interpretation
Conclusion and Future Work
Part IV. Conclusion and Future Work
Chapter 11. Conclusion and Future Work
Evaluation Against the Original Research Questions
Future Directions for e-Science
Chapter A. Namespace Prefixes
Mathematics-specific Issue and Solution Types
Chapter C. Algorithm and Implementation Details
JOBAD, a Library of Assistive Services for Interactive Documents
Transparent Translations in Knowledge Bases
Enabling Collaboration on Semiformal
( Studies on the Semantic Web )
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