Many-Dimensional Modal Logic

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