Full mereogeometries

Review of Symbolic Logic

Volumn 3, Issue 4, 2010, Pages 521-567

  Borgo, Stefano ^a,b   Masolo, Claudio ^a  

^a CNR   (Italy)

^b FREE UNIVERSITY OF BOZEN BOLZANO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79956084122     PISSN: 17550203     EISSN: 17550211     Source Type: Journal    
DOI: 10.1017/S1755020310000110     Document Type: Article

References (61)

1. Asher, N., & Vieu, L. (1995). Toward a geometry of common sense: A semantics and a complete axiomatization of mereotopology. In Mellish, C., editor, Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI 1995). San Francisco: Morgan Kaufmann, pp. 846-852.
2. Aurnague, M., Vieu, L., & Borillo, A. (1997). La Repré sentation Formelle des Concepts Spatiaux dans la Langue. In Denis, M., editor, Langage et Cognition Spatiale. Paris: Masson, pp. 69-102.
3. Bennett, B. (2001). A categorical axiomatisation of region-based geometry. Fundamenta Informaticae, 46, 145-158. (Pubitemid 32551631)
4. Bennett, B., Cohn, A. G., Torrini, P., & Hazarika, S. M. (2000a). Describing rigid body motions in a qualitative theory of spatial regions. In Kautz, H. A., & Porter, B., editors, Proceedings of the National Conference on Artificial Intelligence (AAAI 2000). Menlo Park: AAAI Press/MIT Press, pp. 503-509.
5. Bennett, B., Cohn, A. G., Torrini, P., & Hazarka, S. M. (2000b). A foundation for regionbased qualitative geometry. In Horn,W., editor, Proceedings of the European Conference on Artificial Intelligence (ECAI 2000). Amsterdam: IOS Press, pp. 204-208.
6. Biacino, L., & Gerla, G. (1991). Connection structures. Notre Dame Journal of Formal Logic, 32, 242-247.
7. Biacino, L., & Gerla, G. (1996). Connection structures: Grzegorczyk's and Whitehead's definitions of point. Notre Dame Journal of Formal Logic, 37, 431-439.
8. Borgo, S., Guarino, N., & Masolo, C. (1996). A pointless theory of space based on strong connection and congruence. In Carlucci Aiello, L., Doyle, J., & Shapiro, S. C., editors, Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning (KR 1996). San Francisco: Morgan Kaufmann, pp. 220-229.
9. Casati, R., & Varzi, A. (1999). Parts and Places. The Structure of Spatial Representation. Cambridge: MIT Press.
10. Clarke, B. L. (1981). A calculus of individuals based on connection. Notre Dame Journal of Formal Logic, 22, 204-218.
11. Clarke, B. L. (1985). Individuals and points. Notre Dame Journal of Formal Logic, 26, 61-75.
12. Cohn, A. G. (1995). Qualitative shape representation using connection and convex hulls. In Amsili, P., Borillo, M., & Vieu, L., editors, Proceedings of Time, Space and Movement: Meaning and Knowledge in the Sensible World. Toulouse: IRIT, pp. 3-16 (part C).
13. Cohn, A. G. (2001). Formalising bio-spatial knowledge. InWelty, C., & Smith, B., editors, Proceedings of the International Conference on Formal Ontology in Information Systems (FOIS 2001). New York: ACM Press, pp. 198-209.
14. Cohn, A. G., Bennett, B., Gooday, J., & Gotts, N. (1997a). Representing and reasoning with qualitative spatial relations. In Stock, O., editor, Spatial and Temporal Reasoning. Dordrecht: Kluwer, pp. 97-134.
15. Cohn, A. G., Bennett, B., Gooday, J. M., & Gotts, N. (1997b). RCC: A calculus for region based qualitative spatial reasoning. GeoInformatica, 1, 275-316.
16. Cohn, A. G., & Hazarika, S. M. (2001). Qualitative spatial representation and reasoning: An overview. Fundamenta Informaticae, 46, 1-29. (Pubitemid 32551624)
17. Cohn, A. G., & Varzi, A. (2003). Mereotopological connection. Journal of Philosophical Logic, 32, 357-390.
18. Cristani, M., Cohn, A. G., & Bennet, B. (2000). Spatial locations via morpho-mereology. In Cohn, A. G., Giunchiglia, F., & Selman, B., editors, Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning (KR 2000). San Francisco: Morgan Kaufmann, pp. 15-25.
19. Davis, E. (2006). The expressivity of quantifying over regions. Journal of Logic and Computation, 16, 891-916.
20. Davis, E., Gotts, N., & Cohn, A. G. (1999). Constraint networks of topological relations and convexity. Constraints, 4, 241-280. (Pubitemid 129579726)
21. De Laguna, T. (1922). Point, line, and surface. A sets of solids. The Journal of Philosophy, 19, 449-461.
22. Donnelly, M. (2001). An Axiomatic Theory of Common-Sense Geometry, PhD Thesis, University of Texas.
23. Donnelly, M. (2004). On parts and holes: The spatial structure of the human Body. In Fieschi, M., Coiera, E., & Li, Y.-C. J., editors, Proceedings of MedInfo 2004. Amsterdam: IOS Press.
24. Dugat, V., Gambarotto, P., & Larvor, Y. (1999). Qualitative theory of shape and orientation. In Rodriguez, R. V., editor, Proceedings of the Workshop on Hot Topics in Spatial and Temporal Reasoning, International Joint Conference on Artificial Intelligence (IJCAI 1999). pp. 45-53.
25. Düntsch, I.,Wang, H., & McCloskey, S. (2001) A relation algebraic approach to the region connection calculus. Theoretical Computer Science, 255, 63-83. (Pubitemid 32680442)
26. Galton, A. (1996). Taking dimension seriously in qualitative spatial reasoning. InWahlster, W., editor, Proceedings of the European Conference on Artificial Intelligence (ECAI 1996). Chichester: John Wiley & Sons, pp. 501-505.
27. Galton, A. (2000). Qualitative Spatial Change. New York: Oxford University Press.
28. Galton, A. (2004). Multidimensional mereotopology. In Dubois, D.,Welty, C., &Williams, M.-A., editors, Proceedings of the International Conference on the Principles of Knowledge Representation and Reasoning (KR 2004). Menlo Park: AAAI Press, pp. 45-54.
29. Gerla, G. (1994). Pointless geometries. In Buekenhout, F., editor, Handbook of Incidence Geometry. Amsterdam: Elsevier, pp. 1015-1031.
30. Gotts, N. (1996). Formalizing commonsense topology: The INCH calculus. In Kautz, H., & Selman, B., editors, Proceedings of the International Symposium on Artificial Intelligence and Mathematics (AI/MATH 1996). pp. 72-75.
31. Grzegorczyk, A. (1960). Axiomatizability of geometry without points. Synthese, 12, 228-235.
32. Hodges, W. (1997). A Shorter Model Theory. Cambridge: Cambridge University Press.
33. Knauff, M., Rauh, R., & Renz, J. (1997). A cognitive assessment of topological spatial relations: Results from an empirical investigation. In Hirtle, S. C., & Frank, A. U., editors, Proceedings of the International Conference on Spatial Information Theory (COSIT 1997). Berlin: Springer, pp. 193-206. (Pubitemid 127142683)
34. Li, S., & Ying, M. (2003). Region connection calculus: Its models and composition table. Artificial Intelligence, 145, 121-146.
35. Lobachevskii, N. I. (1835). New principles of geometry with complete theory of parallels (in Russian). Polnoe Sobranie Socinenij, 2.
36. Masolo, C., & Vieu, L. (1999). Atomicity vs. infinite divisibility of space. In Freksa, C., & Mark, D. M., editors, Proceedings of the International Conference on Spatial Information Theory (COSIT 1999). Berlin: Springer, pp. 233-250.
37. Muller, P. (1998a). Éléments d'une théorie du mouvement pour la modélisation du raisonnement spatio-temporel de sens commun., PhD Thesis, Université Paul Sabatier.
38. Muller, P. (1998b). A qualitative theory of motion based on spatio-temporal primitives. In Cohn, A. G., Schubert, L., & Shapiro, S. C., editors, Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning (KR 1998). San Francisco: Morgan Kaufmann, pp. 131-141.
39. Munkres, J. (2000). Topology. Upper Saddle Rivere: Prentice Hall.
40. Nicod, J. (1924). La Géométrie dans le monde sensible. Paris: Presse Universitaire de France.
41. Pratt-Hartmann, I. (1999). First-order qualitative spatial representation languages with convexity. Journal of Spatial Cognition and Computation, 1, 181-204.
42. Pratt-Hartmann, I., & Lemon, O. (1997). Ontologies for plane, polygonal mereotopology. Notre Dame Journal of Formal Logic, 38, 225-245.
43. Pratt-Hartmann, I., & Schoop, D. (1998). A complete axiom system for polygonal mereotopology of the real plane. Journal of Philosophical Logic, 27, 621-658.
44. Pratt-Hartmann, I., & Schoop, D. (2000). Expressivity in polygonal, plane mereotopology. Journal of Symbolic Logic, 65, 822-838.
45. Pratt-Hartmann, I., & Schoop, D. (2002). Elementary polyhedral mereotopology. Journal of Philosophical Logic, 31, 469-498.
46. Randell, D. A., & Cohn, A. G. (1989). Modelling topological and metrical properties in physical processes. In Brachman, R. J., Levesque, H. J., & Reiter, R., editors, Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning (KR 1989). San Francisco: Morgan Kaufmann, pp. 357-368.
47. Randell, D. A., & Cohn, A. G. (1992). A spatial logic based on regions and connections. In Nebel, B., Rich, C., & Swartout, W., editors, Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning (KR 1992). San Francisco: Morgan Kaufmann, pp. 165-176.
48. Renz, J., Rauh, R., & Knauff, M. (2000). Towards cognitive adequacy of topological spatial relations. In Freksa, C., Brauer, W., Habel, C., & Wender, K. F., editors, Spatial Cognition II, Integrating Abstract Theories, Empirical Studies, Formal Methods, and Practical Applications. Berlin: Springer, pp. 184-197.
49. Roeper, P. (1997). Region-based topology. Journal of Philosophical Logic, 26, 251-309.
50. Schmidt, H.-J. (1979). Axiomatic Characterization of Physical Geometry. Berlin- Heidelberg: Springer-Verlag.
51. Schulz, S., & Hahn, U. (2001). Mereotopological reasoning about parts and (w)holes in bio-ontologies. In Welty, C., & Smith, B., editors, Proceedings of the International Conference on Formal Ontology in Information Systems (FOIS 2001). New York: ACM Press, pp. 210-221.
52. Simons, P. (1987). Parts: A Study in Ontology. Oxford: Clarendon Press.
53. Smith, B. (1998). Basic concepts of formal ontology. In Guarino, N., editor, Proceedings of the International Conference on Formal Ontology in Information Systems (FOIS 1998). Amsterdam: IOS Press, pp. 19-28.
54. Smith, B., & Varzi, A. (1999). The niche. Nous, 33, 214-238.
55. Stell, J. G. (2000). Boolean connection algebras; a new approach to the region-connection calculus. Artificial Intelligence, 122, 111-136.
56. Stock, O., editor. (1997). Spatial and Temporal Reasoning. Dordrecht: Kluwer Academic Publishers.
57. Tarski, A. (1956a). Foundations of the geometry of solids. In Corcoran, J., editor, Logic, Semantics, Metamathematics. Oxford: Oxford University Press, pp. 24-30.
58. Tarski, A. (1956b). A general theorem concerning primitive notions of Euclidean geometry. Indagationes Mathematicae, 18, 468-474.
59. Van Benthem, J. (1983). The Logic of Time. Dordrecht: Kluwer.
60. Vieu, L. (1997). Spatial representation and reasoning in artificial intelligence. In Stock, O., editor, Spatial and Temporal Reasoning. Dordrecht: Kluwer, pp. 5-41.
61. Whitehead, A. N. (1929). Process and Reality. An Essay in Cosmology. New York: Macmillan.