Abstract
We investigate the major mathematical theories of space from a modal standpoint: topology, affine geometry, metric geometry, and vector algebra. This allows us to see new finestructure in spatial patterns which suggests analogies across these mathematical theories in terms of modal, temporal, and conditional logics. Throughout the modal walk through space, expressive power is analyzed in terms of language design, bisimulations, and correspondence phenomena. The result is both unification across the areas visited, and the uncovering of interesting new questions.
| Original language | English |
|---|---|
| Pages (from-to) | 319-363 |
| Number of pages | 45 |
| Journal | Journal of Applied Non-Classical Logics |
| Volume | 12 |
| Issue number | 3-4 |
| DOIs | |
| Publication status | Published - 2002 |
| Externally published | Yes |
Keywords
- Affine geometry
- Arrow logics
- Conditional logic
- Elementary geometry
- Linear logic
- Mathematical morphology
- Modal logics
- Spatial reasoning
- Topology