Pretopologies and Dynamic Spaces

• Autorzy: Pagliani, P.
• Języki publikacji: EN

Abstrakty

EN

Approximation Spaces were introduced in order to analyse data on the basis of Indiscernibility Spaces, that is, spaces of the form < U,E > , where U is a universe of items and E is an equivalence relation on U. Various authors suggested to consider spaces of the form < U,R > , where R is any binary relation. This paper aims at introducing a further step consisting in taking into account spaces of the form < U,{R_i}_i€I> , where {R_ii€I is a family of binary relations, that we call "Dynamic Spaces" because by means of this generalisation we can account for different forms of dynamics. While Indiscernibility Spaces induce 0-dimensional topological spaces (Approximation Spaces), Dynamic Spaces induce various types of pre-topological spaces.

Słowa kluczowe

EN

pretopologies; relations; approximation space; dynamic

• Czasopismo: Fundamenta Informaticae
• Rocznik: 2004
• Tom: Vol. 59, nr 2,3
• Strony: 221-239
• Opis fizyczny: Bibliogr. 15 poz., tab.

Twórcy

autor

Pagliani, P.

• Research Group on Knowledge and Communication Models, Via Imperia, 6, 00161 Rome, Italy,

Bibliografia

• [1] Belmandt, Z.: Manuel de prétopologie et set applications. Hermes, 1993.
• [2] Ben David S., Brezner O. and Francez N.: An Expectation Modal Logic. Technical Report. Computer Science Dept. Technion, Haifa, Israel.
• [3] Cech E.: Topological Spaces. John Wiley and Sons. 1966.
• [4] Chellas B.: Modal Logic: An Introduction. Cambridge University Press. 1980.
• [5] Langeron C. and Bonnevay S.: Une approche pretopologique pour la structuration. Centre de recherches économiques. Université de Sait-Etienne. Documente de recherche 1999-7. http://www.univ-st-etienne.fr/creuset/membres/largeron-leteno-christine.htm
• [6] Lin T. Y.: Granular Computing on Binary Relations. I and II. In Polkowski L. and Skowron A. (Eds.) Rough Sets in Knowledge Discovery. 1: Methodology and Applications. Physica-Verlag. 1988, pp. 107-121 and 122-140.
• [7] Montague R. : Pragmatics. In Klibanski R. (Ed.) Contemporary Philosophy. A Survey, La Nuova Italia Editrice, 1968, pp. 102-122.
• [8] Pagliani P.: Moralizing Relations by means of Relations: a general framework for two basic approaches to Knowledge Discovery in Database. In Proceeding of IPMU ’98, July. 6-10, 1998. ”La Sorbonne’, Paris, France, pp. 1175-1182.
• [9] Pagliani P.: Concrete neighbourhood systems and formal pretopological spaces. (Draft, 2002).
• [10] Pawlak, Z.: Rough sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Publisher, 1991.
• [11] Sambin G. and Gebellato S.: A Preview of the Basic Picture: A New Perspective on Formal Topology. TYPES 1998. pp. 194-207.
• [12] Skowron A. and Stepaniuk J.: Approximation of Relations. In W. Ziarko (ed.): Rough Sets, Fuzzy Sets and Knowledge Discovery, Springer-Verlag, 1994, pp. 161-166.
• [13] Scott D.: Advice on Modal Logic. In Lambert K. (Ed.) Philosophical Problems in Logic. Reidel, 1970. pp.143-173.
• [14] Stadler В. M. R. and Stadler P F.: Generalised Topological Spaces in Evolutionary Theory and Combinatorial Chemistry. Technical Report, Institut für Theoretische Chemie und Molekulare Strukturbiologie, Wien University, 2001.
• [15] Yao Y. Y. and Lin T. Y.: Graded Rough Set Approximations based on Nested Neighborhood Systems. In Proceeding of EUFIT '91. Vol 1. ELIT-Foundation, Aachen, 1997, pp. 196-200.