Point-free Foundation of Geometry and Multivalued Logic
Coppola, Cristina ; Gerla, Giangiacomo ; Miranda, Annamaria
Notre Dame J. Formal Logic, Tome 51 (2010) no. 1, p. 383-405 / Harvested from Project Euclid
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Whitehead, in two basic books, considers two different approaches to point-free geometry: the inclusion-based approach, whose primitive notions are regions and inclusion relation between regions, and the connection-based approach, where the connection relation is considered instead of the inclusion. We show that the latter cannot be reduced to the first one, although this can be done in the framework of multivalued logics.
Publié le : 2010-07-15
Classification:  foundation of geometry,  point-free geometry,  Whitehead,  multivalued logic,  03B30,  18A15,  54E99 
@article{1282137990,
     author = {Coppola, Cristina and Gerla, Giangiacomo and Miranda, Annamaria},
     title = {Point-free Foundation of Geometry and Multivalued Logic},
     journal = {Notre Dame J. Formal Logic},
     volume = {51},
     number = {1},
     year = {2010},
     pages = { 383-405},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1282137990}
}

Coppola, Cristina; Gerla, Giangiacomo; Miranda, Annamaria. Point-free Foundation of Geometry and Multivalued Logic. Notre Dame J. Formal Logic, Tome 51 (2010) no. 1, pp.  383-405. http://gdmltest.u-ga.fr/item/1282137990/