Special Issue on point-free geometry and topology. An introduction
DOI:
https://doi.org/10.12775/LLP.2013.008Słowa kluczowe
mereology, Boolean algebras, point-free geometry, point-free topology, intuitionism, category theory, multi-valued logic, decidabilityAbstrakt
In the first section we briefly describe methodological assumptions of point-free geometry and topology. We also outline history of geometrical theories based on the notion of \emph{region}. The second section is devoted to concise presentation of the content of the LLP special issue on point-free theories of space.
Bibliografia
Casati R., and A. Varzi, “Spatial entities”, in Spatial and Temporal Reasoning, Oliviero Stock (ed.), Dordrecht, Kluwer, 1997, pp. 73–96 .
Clarke, B., “A calculus of individuals based on connection”, Notre Dame Journal of Formal Logic, 22 (1981), 3: 204–218.
Clarke, B., “Individuals and points”, Notre Dame Journal of Formal Logic, 26 (1985), 1: 61–75.
De Laguna, T., “Point, line and surface as sets of solids”, The Journal of Philosophy, 19 (1922): 449–461.
Gerla, G., “Pointless geometries”, in Handbook of Incidence Geometry, F. Buekenhout (ed.), Elsevier Science, 1994, pp. 1015–1031.
Gerla, G., and B. Paolillo, “Whitehead’s point-free geometry and diametric posets”, Logic and Logical Philosophy, 19 (2010): 289–308.
Grzegorczyk, A., “Axiomatization of geometry without points”, Synthese, 12 (1960): 228–235.
Gruszczyński, R., and A. Pietruszczak, “Full development of Tarski’s geometry of solids”, The Bulletin of Symbolic Logic, 14 (2008), 4: 481–540.
Lobachevskii, N.I., “New principles of geometry with complete theory of parallels” (in Russian), Polnoe Sobranie Socinenij, 2 (1835).
Tarski, A., “Foundations of the geometry of solids”, in Logic, Semantics, Metamathematics, J. Corcoran (ed.), Oxford University Press, Oxford, 1956, pp. 24–30. Translation of: “Les fondaments de la géométrie des corps”, in Księga Pamiątkowa Pierwszego Polskiego Zjazdu Matematycznego, 3 (1929), pp. 29–33.
Whitehead, A.N., An Inquiry Concerning the Principles of Natural Knowledge, Univ. Press. Cambrige, 1919.
Whitehead, A.N., The Concept of Nature, Univ. Press. Cambrige, 1920.
Whitehead, A.N., Process and Reality, Macmillan, 1929, N.Y.
Pobrania
Opublikowane
Jak cytować
Numer
Dział
Statystyki
Liczba wyświetleń i pobrań: 565
Liczba cytowań: 1
