Logic for physical space: From antiquity to present days

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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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
JournalSynthese
Publication date2012
Volume186
Issue3
Pages619-632
ISSN0039-7857
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 0

Keywords

  • Modal logic, Geometry, Topology, Mathematical morphology
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