We suggest possible approaches to point-free geometry based on multi- valued logic. The idea is to assume as primitives the notion of region together with suitable ‘vague’ predicates whose meaning is geometrical in nature. For example, predicates as ‘close’, ‘small’, ‘contained’. In accordance, 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 in account that very interesting metrical approaches to geometry exist (see for example Blumenthal’s book [2]), 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 furnishes a tool to illustrate the passage from a naive and ‘qualitative’ approach to geometry to a ‘quantitative’ one of advanced science.

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

coppola cristina;GERLA, Giangiacomo
2015-01-01

Abstract

We suggest possible approaches to point-free geometry based on multi- valued logic. The idea is to assume as primitives the notion of region together with suitable ‘vague’ predicates whose meaning is geometrical in nature. For example, predicates as ‘close’, ‘small’, ‘contained’. In accordance, 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 in account that very interesting metrical approaches to geometry exist (see for example Blumenthal’s book [2]), 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 furnishes a tool to illustrate the passage from a naive and ‘qualitative’ approach to geometry to a ‘quantitative’ one of advanced science.
2015
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4717182
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 0
social impact