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

• Authors: Coppola Cristina , Gerla Giangiacomo
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

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

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2015
• Volume: 24
• Issue: 4 Mereology and Beyond
• Pages: 535-553

Dates

online

2015-11-13

Contributors

author

Coppola Cristina

• Dipartimento di Matematica, Università degli Studi di Salerno

author

Gerla Giangiacomo

• Dipartimento di Matematica, Università degli Studi di Salerno

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Identifiers

DOI

10.12775/LLP.2015.019