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Logic and Logical Philosophy

Mereological foundations of point-free geometry via multi-valued logic
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Mereological foundations of point-free geometry via multi-valued logic

Authors

  • Cristina Coppola Università degli Studi di Salerno
  • Giangiacomo Gerla Università degli Studi di Salerno

DOI:

https://doi.org/10.12775/LLP.2015.019

Keywords

point-free geometry, multi-valued logic, fuzzy logic, continuous logic, metric geometry, mereology, naïve science

Abstract

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.

Author Biographies

Cristina Coppola, Università degli Studi di Salerno

Dipartimento di Matematica

Giangiacomo Gerla, Università degli Studi di Salerno

Dipartimento di Matematica

References

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Logic and Logical Philosophy

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Published

2015-11-13

How to Cite

1.
COPPOLA, Cristina and GERLA, Giangiacomo. Mereological foundations of point-free geometry via multi-valued logic. Logic and Logical Philosophy. Online. 13 November 2015. Vol. 24, no. 4, pp. 535-553. [Accessed 3 July 2025]. DOI 10.12775/LLP.2015.019.
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