A modalwalk through space

Journal of Applied Non-Classical Logics

Volumn 12, Issue 3-4, 2002, Pages 319-363

  Aiello, Marco ^a   Van Benthem, Johan ^a  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

Affine geometry; Arrow logics; Conditional logic; Elementary geometry; Linear logic; Mathematical morphology; Modal logics; Spatial reasoning; Topology

Indexed keywords

EID: 0346261133     PISSN: 11663081     EISSN: 19585780     Source Type: Journal    
DOI: 10.3166/jancl.12.319-363     Document Type: Article

References (68)

1. [AIE 01] AIELLO M., VAN BENTHEM J., BEZHANISHVILI G., "Reasoning about Space: the Modal Way" report num. PP-2001-18, 2001, ILLC, University of Amsterdam, Submitted to the Journal of Logic and Computation.
2. [AIE 02a] AIELLO M., "Spatial Resoning: Theory and Practice" PhD thesis, University of Amsterdam, 2002, DS-2002-02.
3. [AIE 02b] AIELLO M., "A Spatial Similarity based on Games: Theory and Practice" Journal of the Interest Group in Pure and Applied Logic, vol. 10, num. 1, 2002, p. 1-22, Oxford University Press.
4. [AIE 02c] AIELLO M., VAN BENTHEM J., "Logical Patterns in Space" BARKER-PLUMMER D., BEAVER D., VAN BENTHEM J., SCOTTO DI LUZIO P., Eds., Words, Proofs, and Diagrams, CSLI, Stanford, 2002, To appear.
5. [ALL 83] ALLEN J., "Maintaining knowledge about temporal intervals" Communications of the ACM, vol. 26, 1983, p. 832-843.
6. [ALL 85] ALLEN J., HAYES P., "A common sense theory of time" JOSHI A., Ed., IJCAI85, vol. 1, International Joint Conference on Artificial Itelligence, Morgan Kaufmann, 1985, p. 528-531.
7. [ARE 00] ARECES C., "Logic Engineering: The Case of Description and Hybrid Logics" PhD thesis, University of Amsterdam, 2000.
8. [ASH 95] ASHER N., VIEU L., "Toward a Geometry of Common Sense: a semantics and a complete axiomatization of mereotopology" IJCAI95, International Joint Conference on Artificial Itelligence, 1995, p. 846-852.
9. [BAL 97] BALBIANI P., FARIÑAS DEL CERRO L., TINCHEV T., VAKARELOV D., "Modal logics for incidence geometries" Journal of Logic and Computation, vol. 7, 1997, p. 59-78. (Pubitemid 127670055)
10. [BAL 98] BALBIANI P., "The modal multilogic of geometry" Journal of Applied Non- Classical Logics, vol. 8, 1998, p. 259-281.
11. [BEN ] VAN BENTHEM J., "Logical structures in mathematical morphology" Available at http://www.science.uva.nl/~johan/MM-LL.ps.
12. [BEN 83a] VAN BENTHEM J., "Correspondence Theory" GABBAY D., GUENTHNER F., Eds., Handbook of Philosophical Logic, vol. II, p. 167-247, Reidel Publishing Company, 1983.
13. [BEN 83b] VAN BENTHEM J., The Logic of Time, vol. 156 of Synthese Library, Reidel, Dordrecht, 1983, [Revised and expanded, Kluwer, 1991].
14. [BEN 83c] VAN BENTHEM J., DOETS K., "Higher-Order Logic" GABBAY D., GUENTHNER F., Eds., Handbook of Philosophical Logic, vol. 1, p. 275-329, Reidel Publishing Company, 1983.
15. [BEN 86] BEN-OR M., KOZEN D., J.REIF, "The Complexity of Elementary Algebra and Geometry" Journal of Computer and System Sciences, vol. 32, 1986, p. 251-264.
16. [BEN 91a] VAN BENTHEM J., Language in Action. Categories, Lambdas and Dynamic Logic, North-Holland, Amsterdam, 1991.
17. [BEN 91b] VAN BENTHEM J., "Logic and the flow of information" PRAWITZ D., SKYRMS B., WESTERTAL D., Eds., Proceedings of the 9th International Conference of Logic, Methodology and Philosophy of Science, Elsevier, 1991, p. 693-724.
18. [BEN 95] BENNETT B., "Modal Logics for Qualitative Spatial Reasoning" Bulletin of the IGPL, vol. 3, 1995, p. 1-22.
19. [BEN 96] VAN BENTHEM J., Exploring Logical Dynamics, vol. 156, CSLI Publications, Stanford | Cambridge University Press, 1996.
20. [BEN 02] VAN BENTHEM J., BEZHANISHVILI G., GEHRKE M., "Euclidean Hierarchy in Modal Logic" report num. PP-2002-8, 2002, Univ. of Amsterdam.
21. [BLA 01] BLACKBURN P., DE RIJKE M., VENEMA Y., Modal Logic, Cambridge University Press, 2001.
22. [BLO 00] BLOCH I., "Using Mathematical Morphology Operators as Modal Operators for Spatial Reasoning" ECAI 2000, Workshop on Spatio-Temporal Reasoning, 2000, p. 73-79.
23. [BLU 61] BLUMENTHAL L., A Modern View of Geometry, Dover, 1961.
24. [BUR 84] BURGESS J., "Basic Tense Logic" GABBAY D., GUENTHNER F., Eds., Handbook of Philosophical Logic, vol. II, chapter 2, p. 89-133, Reidel, 1984.
25. [CAS 99] CASATI R., VARZI A., Parts and Places, MIT Press, 1999.
26. [CLA 81] CLARKE B., "A calculus of individuals based on 'connection"', Notre Dame Journal of Formal Logic, vol. 23, num. 3, 1981, p. 204-218.
27. [DAB 96] DABROWSKI A., MOSS A., PARIKH R., "Topological reasoning and the logic of knowledge" Annals of Pure and Applied Logic, vol. 78, 1996, p. 73-110. (Pubitemid 126160878)
28. [DOE 87] DOETS K., "Completeness and Definability. Applications of the Ehrenfeucht Game in Second-Order and Intensional Logic" PhD thesis, ILLC, University of Amsterdam, 1987.
29. [GAB 94] GABBAY D., HODKINSON I., REYNOLDS M., Temporal Logic: Mathematical Foundations and Computational Aspects, vol. 1, Oxford University Press, 1994.
30. [GÄR 00] GÄRDENFORS P., Conceptual Spaces, MIT Press, 2000.
31. [GEO 93] GEORGATOS K., "Modal Logics for Topological Spaces" PhD thesis, City University of New York, 1993.
32. [GIR 87] GIRARD J.-Y., "Linear logic" Theoretical Computer Science, vol. 50, 1987, p. 1-102.
33. [GOL 87] GOLDBLATT R., Orthogonality and Spacetime Geometry, Springer-Verlag, 1987.
34. [GOR 92] GORANKO V., PASSY S., "Using the universal modality: gains and questions" Journal of Logic and Computation, vol. 2, 1992, p. 5-30.
35. [HAM 95] HAMMER E., Logic and Visual Information, CSLI and FoLLi, Stanford, 1995.
36. [HAR 83] HAREL D., "Recurring Dominoes: Making the highly undecidable highly understandable" Conference on Foundations of Computer Science, vol. LNCS 158, Springer, 1983, p. 177-194.
37. [HEI 94] HEIJMANS H. J. A. M., Morphological Image Operators, Academic Press, Boston, 1994.
38. [HEL 23] HELLY E., "Über Mengen konvexer K orper mit gemeinschaftlichen Punkten" Jahresber. Deutsch. Math.- Verein, vol. 32, 1923, p. 175-176.
39. [KAM 68] KAMP J., "Tense logic and the theory of linear order" PhD thesis, University of California, Los Angeles, 1968.
40. [KER 01] KERDILES G., "Saying It with Pictures: a logical landscape of coneptual graphs" PhD thesis, Univeristy of Amsterdam, 2001.
41. [KUR 95] KURTONINA N., "Frames and Labels. A Modal Analysis of Categorial Inference" PhD thesis, ILLC, Amsterdam, 1995.
42. [KUR 97] KURTONINA N., DE RIJKE M., "Bisimulations for Temporal Logic" Journal of Logic, Language and Information, vol. 6, 1997, p. 403-425.
43. [LES 83] LESNIEWSKI S., "The foundation of mathematics" Topoi, vol. 2, 1983, p. 7-52, Translation of the paper of 1931.
44. [LEW 73] LEWIS D., Counterfactuals, Harvard University Press, 1973.
45. [MAR 97] MARX M., VENEMA Y., Multi Dimensional Modal Logic, Kluwer, 1997.
46. [MAT 67] MATHERON G., Eléments pur une theorie des milieux poreaux, Masson, 1967.
47. [MCK 44] MCKINSEY J., TARSKI A., "The Algebra of Topology" Annals of Mathematics, vol. 45, 1944, p. 141-191.
48. [MIN 98] MINTS G., "A Completeness Proof for Propositional S4 in Cantor space" E. ORLOWSKA, Ed., Logic at work : Essays dedicated to the memory of Helena Rasiowa, Physica-Verlag, Heidelberg, 1998.
49. [NUT 83] NUTE D., "Conditional Logic" GABBAY D., GUENTHNER F., Eds., Handbook of Philosophical Logic, vol. IV, p. 387-439, Reidel Publishing Company, 1983.
50. [PLA 95] VON PLATO J., "The Axioms of Constructive Geometry" Annals of Pure and Applied Logic, vol. 76, num. 2, 1995, p. 169-200.
51. [PRE 85] PREPARATA F., SHAMOS M., Computational Geometry: An Introduction, Springer- Verlag, 1985.
52. [RAN 92] RANDELL D., CUI Z., COHN A. G., "A Spatial Logic Based on Regions and Connection" Proc. of Int. Conf. on Principles of Knowledge Representation and Reasoning (KR'92), San Mateo, 1992, p. 165-176.
53. [RAN 01] RANDELL D., WITKOWSKI M., SHANAHAN M., "From Images to Bodies: Modelling and Exploiting Occlusion and Motion Parallax" Proc. of Int. Joint Conference on Artificial Intelligence (IJCAI-01), 2001.
54. [RAS 63] RASIOWA H., SIKORSKI R., The Mathematics of Metamatematics, Panstwowe Wydawnictwo naukowe, 1963.
55. [RIJ 93] DE RIJKE M., "Extended Modal Logic" PhD thesis, ILLC, University of Amsterdam, 1993.
56. [SEG 70] SEGERBERG K., "Modal Logics with linear alternative relations" Theoria, vol. 36, 1970, p. 301-322.
57. [SER 82] SERRA J., Image Analysis and Mathematical Morphology, Academic Press, 1982.
58. [SHE 99] SHEHTMAN V., ""Everywhere" and "Here"" Journal of Applied Non-Classical Logics, vol. 9, num. 2-3, 1999, p. 369-379.
59. [STE 00] STEBLETSOVA V., "Algebras, relations and Geometries" PhD thesis, University of Utrecht, 2000.
60. [SZC 65] SZCZERBA L., TARSKI A., "Metamathematical properties of some affine geometries" BAR-HILLEL Y., Ed., Int. Congress for Logic, Methodolog, and Philosophy of Science, North-Holland, 1965, p. 166-178.
61. [TAR 38] TARSKI A., "Der Aussagenkalkül und die Topologie" Fund. Math., vol. 31, 1938, p. 103-134.
62. [TAR 59] TARSKI A., "What is Elementary Geometry?" L. HENKIN AND P. SUPPES AND A. TARSKI, Ed., The Axiomatic Method, with Special Reference to Geometry ad Physics, p. 16-29, North-Holland, 1959.
63. [TRO 92] TROELSTRA A. S., Lectures on Linear Logic, CSLI, 1992.
64. [VEL 85] VELTMAN F., "Logics for conditionals" PhD thesis, University of Amsterdam, 1985.
65. [VEN 92] VENEMA Y., "Many-Dimensional Modal Logic" PhD thesis, ILLC, University of Amsterdam, 1992.
66. [VEN 96] VENEMA Y., "A crash course in Arrow Logic" MARX M., MASUCH M., PÓLOS L., Eds., Arrow Logic and Multimodal Logic, CSLI, 1996.
67. [VEN 99] VENEMA Y., "Points, Lines and Diamonds: a Two-Sorted Modal Logic for Projective Planes" Journal of Logic and Computation, vol. 9, num. 5, 1999, p. 601-621. (Pubitemid 30553022)
68. [WHI 29] WHITEHEAD A., Process and Reality, The MacMillan Company, New York, 1929.