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Many-Dimensional Modal Logic

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This is a doctoral dissertation of Yde Venema under the supervision of prof. Johan van Benthem.

Author(s): Yde Venema
Series: Historical Dissertations Series, 4
Publisher: University of Amsterdam
Year: 1992

Language: English
Commentary: Scanned, DjVu'ed, OCR'ed, TOC by Envoy
Pages: 184

Chapter 1. Dimensions in Modal Logic

Chapter 2. Rules for the Undefinable

2.1. Introduction
2.2. Sahlqvist theorems
2.3. Sahlqvist tense formulas
2.4. The D-operator
2.5. The Main Proof
2.6. Uni-directional complications
2.7. The SD-theorem
2.8. The SNS-theorem
2.9. Conclusions, remarks and questions

Chapter 3. The Square Universe

3.1. Introduction
3.2. Two-dimensional cylindric logic
3.3. A modal logic of binary relations
3.4. A two-dimensional temporal logic
3.5. Two-dimensional algebras
3.6. Conclusions, remarks and questions

Chapter 4. Quantifiers and Cubes

4.1. Algebraizing restricted first order logic
4.2. Cylindric modal logic
4.3. Characterizing n-cubes
4.4. Axiomatizing n-cubes
4.5. Harvest
4.6. Using the Dn-irreflexivity rule
4.7. Conclusions, remarks and questions

Chapter 5. Periods in Planes

5.1. Introduction
5.2. The system HS
5.3. Intervals as computation paths
5.4. A modal operator for chopping intervals
5.5. Conclusions, remarks and questions

Chapter 6. Conclusions

Appendix A. Modal Similarity Types

Appendix B. Consequences of Derivation Systems