Notre Dame Journal of Formal Logic

Point-free Foundation of Geometry and Multivalued Logic

Cristina Coppola, Giangiacomo Gerla, and Annamaria Miranda

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 18 August 2010

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1282137990

Digital Object Identifier
doi:10.1215/00294527-2010-024

Zentralblatt MATH identifier
05773619

Mathematical Reviews number (MathSciNet)
MR2675690

Subjects
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

Keywords
foundation of geometry point-free geometry Whitehead multivalued logic

Citation

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. http://projecteuclid.org/euclid.ndjfl/1282137990.


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References

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