Representation Theorems in Computer Science

1. Front Matter

   Pages i-xiii

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2. Introduction

   • Özgür Lütfü Özçep

   Pages 1-17

3. Preliminaries

   • Özgür Lütfü Özçep

   Pages 19-40

4. Representing Spatial Relatedness

   • Özgür Lütfü Özçep

   Pages 41-73

5. Scalable Spatio-Thematic Query Answering

   • Özgür Lütfü Özçep

   Pages 75-97

6. Representation Theorems for Stream Processing

   • Özgür Lütfü Özçep

   Pages 99-128

7. High-Level Declarative Stream Processing

   • Özgür Lütfü Özçep

   Pages 129-150

8. Representation for Belief Revision

   • Özgür Lütfü Özçep

   Pages 151-181

9. Conclusion

   • Özgür Lütfü Özçep

   Pages 183-187

Formal specifications are an important tool for the construction, verification and analysis of systems, since without it is hardly possible to explain whether a system worked correctly or showed an expected behavior. This book proposes the use of representation theorems as a means to develop an understanding of all models of a specification in order to exclude possible unintended models, demonstrating the general methodology with representation theorems for applications in qualitative spatial reasoning, data stream processing, and belief revision.


For qualitative spatial reasoning, it develops a model of spatial relatedness that captures the scaling context with hierarchical partitions of a spatial domain, and axiomatically characterizes the resulting relations. It also shows that various important properties of stream processing, such as prefix-determinedness or various factorization properties can be axiomatized, and that the axioms are fulfilled by natural classes of stream functions. The third example is belief revision, which is concerned with the revision of knowledge bases under new, potentially incompatible information. In this context, the book considers a subclass of revision operators, namely the class of reinterpretation operators, and characterizes them axiomatically. A characteristic property of reinterpretation operators is that of dissolving potential inconsistencies by reinterpreting symbols of the knowledge base.


Intended for researchers in theoretical computer science or one of the above application domains, the book presents results that demonstrate the use of representation theorems for the design and evaluation of formal specifications, and provide the basis for future application-development kits that support application designers with automatically built representations.

• Description Logics
• Ontology Engineering
• Temporal Reasoning
• Non-monotonic Reasoning
• Spatial-Temporal Systems
• Stream Processing
• Semantics and Reasoning

• Institute of Information Systems , University of Lübeck, Lübeck, Germany

  Özgür Lütfü Özçep

​Özgür L. Özçep is a researcher and lecturer (Privatdozent) at the University of Lübeck. His research as well as his teaching covers foundational aspects of computer science with a focus on logical and mathematical modelling for AI related domains and problems. He has published in the areas of belief revision, description logics, ontologies, qualitative spatial reasoning, and stream processing.

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