Logic for physical space: From antiquity to present days

Synthese 186 (3):619-632 (2012)

Authors
Valentin Goranko
Stockholm University
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
Keywords Modal logic  Geometry  logics of space  Mathematical morphology
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DOI 10.1007/s11229-011-9913-9
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References found in this work BETA

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - Cambridge University Press.
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
Model Theory.Wilfrid Hodges - 2008 - Stanford Encyclopedia of Philosophy.
Tarski's System of Geometry.Alfred Tarski & Steven Givant - 1999 - Bulletin of Symbolic Logic 5 (2):175-214.

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