| This is a file in the archives of the Stanford Encyclopedia of Philosophy. |
2. Note that, however natural this convention may sound, this is still an arbitrary convention. For example, Lambert and Englebretsen's systems visualize individuals as points and sets as lines [Lambert 1764, Englebretsen 1992].
3. Euler [1768], p. 233.
4. For more details, see Hammer and Shin [1998].
5. Such problems have been studied under the banner of “Topological Inference ” and are nearly all NP hard [Grigni et al. 1995, Lemon & Pratt 1997b, Lemon 2001].
6. Now Ian Pratt-Hartmann.
7. As a practical instance of Helly's Theorem.
8. For more recent logical study on this issue, refer to papers by Aiello and van Benthem, Fisler, and Lemon, in Barker-Plummer et al. [2002].
9. For example: Reasoning with Diagrammatic Representations: 1992 AAAI Spring Symposium; Cognitive and Computational Models of Spatial Representation: 1996 AAAI Spring Symposium; Reasoning with Diagrammatic Representations II: 1997 AAAI Fall Symposium; and Formalizing Reasoning with Visual and Diagrammatic Representations: 1998 AAAI Fall Symposium. See also Narajanan [1993].
10. The following conferences are good evidence for this effort: VISUAL '98: Visualization Issues in Formal Methods (Lisbon); International Roundtable Conference on Visual and Spatial Reasoning in Design (MIT, 1999); and Theories of Visual Languages -- Track of VL '99 : 1999 IEEE Symposium on Visual Languages.
11. See Aristotle On the Soul and On the Memory and Recollection.
12. Block [1981] is one of the best collections of important papers on this debate, and Block [1983] presents a succinct summary of this controversy and raises insightful philosophical questions about the debate. Chapters 1-4 of Tye [1991] are a good overview of both cognitive scientists' and philosophers' various positions on this issue.
| Sun-Joo Shin Sun-Joo.Shin@yale.edu | Oliver Lemon olemon@inf.ed.ac.uk |