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Tuesday, December 30, 2003

A Generalization Hierarchy of Theories 

From topicmapmail: via Murray Altheim
 ~-----------------------------------------------------------------~
   |                                                                 |
   |                 Tautologies                                     |
   |         ________/  |  \________________                         |
   |        /           |   \               \                        |
   |       /            |    \               \                       |
   |   Antisymmetry     |     \          Symmetry                    |
   |       \            |      \             /                       |
   |        \   Transitivity  Reflexivity   /                        |
   |         \        /    \  /   |        /                         |
   |          \      /      \/    |       /                          |
   |           \    /       /\    |      /                           |
   |            \  /       /  \   |     /                            |
   |         PartialOrdering  Equivalence                            |
   |           /      \                                              |
   |          /        \                                             |
   |       Trees      Lattices                                       |
   |         \          /    \_______________                        |
   |          \        /      |      \       \                       |
   |           \      /       |       \       \                      |
   |      LinearOrdering  Theories  Types  Collections               |
   |        /    \               ___________/    \                   |
   |       /      \             /                 \                  |
   |  Sequences  Numbers     Sets              Mereology             |
   |      \      / \        /   \              /   |   \             |
   |       \    /   \      /     \            /    |    \            |
   |    Integers  Reals  ZF-Sets  VNGB-Sets  /     |     \           |
   |                                        /      |      \          |
   |                                   Discrete  Lumpy  Continuous   |
   |                                                                 |
   ~-----------------------------------------------------------------~
   Figure 2.14: A generalization hierarchy of theories
                from "Knowledge Representation", John Sowa (p.95)


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