Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We suggest possible approaches to point-free geometry based on multi-valued logic. The idea is to assume as primitives the notion of a region together with suitable vague predicates whose meaning is geometrical in nature, e.g. ‘close’, ‘small’, ‘contained’. Accordingly, some first-order multi-valued theories are proposed. We show that, given a multi-valued model of one of these theories, by a suitable definition of point and distance we can construct a metrical space in a natural way. Taking into account that interesting metrical approaches to geometry exist, this looks to be promising for a point-free foundation of the notion of space. We hope also that this way to face point-free geometry provides a tool to illustrate the passage from a naïve and ‘qualitative’ approach to geometry to the ‘quantitative’ approach of advanced science.
Czasopismo
Rocznik
Tom
Numer
Strony
535-553
Opis fizyczny
Daty
online
2015-11-13
Twórcy
autor
- Dipartimento di Matematica, Università degli Studi di Salerno, ccoppola@unisa.it
autor
- Dipartimento di Matematica, Università degli Studi di Salerno, gerla@unisa.it
Bibliografia
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- Coppola, C., and G. Gerla, “Special issue on point-free geometry and topology: An introduction”, Logic and Logical Philosophy, 22 (2013): 139–143. DOI: 10.12775/LLP.2013.008
- Coppola, C., and G. Gerla, “Multi-valued logic for a point-free foundation of geometry”, pages 105–122 in: Mereology and the Sciences. Parts and Wholes in the Contemporary Scientific Context., C. Calosi and P. Graziani (eds.), Springer Synthese Library, vol. 372, 2014. DOI: 10.1007/978-3-319-05356-1_5
- Coppola, C., G. Gerla, and A. Miranda, “Point-free foundation of geometry and multi-valued logic”, Notre Dame Journal of Formal Logic, 51, 3 (2010): 383–405. DOI: 10.1215/00294527-2010-024
- Di Concilio, A., and G. Gerla, “Quasi-metric spaces and point-free geometry”, Mathematical Structures in Computer Science, 16, 1 (2006): 115–137. DOI: 10.1017/S0960129506005111
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- Gerla, G., and B. Paolillo, “Whitehead’s point-free geometry and diametric posets”, Logic and Logical Philosophy, 19 (2010): 289–308. DOI:10.12775/LLP.2010.010
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Typ dokumentu
Bibliografia
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