Notre Dame Journal of Formal Logic

Point-free Foundation of Geometry and Multivalued Logic

Cristina Coppola, Giangiacomo Gerla, and Annamaria Miranda


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.

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Notre Dame J. Formal Logic Volume 51, Number 3 (2010), 383-405.

First available in Project Euclid: 18 August 2010

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Zentralblatt MATH identifier

Primary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35] 18A15: Foundations, relations to logic and deductive systems [See also 03- XX]
Secondary: 54E99: None of the above, but in this section

foundation of geometry point-free geometry Whitehead multivalued logic


Coppola, Cristina; Gerla, Giangiacomo; Miranda, Annamaria. Point-free Foundation of Geometry and Multivalued Logic. Notre Dame J. Formal Logic 51 (2010), no. 3, 383--405. doi:10.1215/00294527-2010-024.

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