Logic for physical space: From antiquity to present days

Marco Aiello*, Guram Bezhanishvili, Isabelle Bloch, Valentin Goranko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Since the early days of physics, space has called for means to represent, experiment, and reason about it. Apart from physicists, the concept of space has intrigued also philosophers, mathematicians and, more recently, computer scientists. This longstanding interest has left us with a plethora of mathematical tools developed to represent and work with space. Here we take a special look at this evolution by considering the perspective of Logic. From the initial axiomatic efforts of Euclid, we revisit the major milestones in the logical representation of space and investigate current trends. In doing so, we do not only consider classical logic, but we indulge ourselves with modal logics. These present themselves naturally by providing simple axiomatizations of different geometries, topologies, space-time causality, and vector spaces.

Original languageEnglish
Pages (from-to)619-632
Number of pages14
JournalSynthese
Volume186
Issue number3
DOIs
Publication statusPublished - Jun 2012
Externally publishedYes

Keywords

  • Geometry
  • Mathematical morphology
  • Modal logic
  • Topology

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