, Volume 186, Issue 3, pp 619-632

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Logic for physical space

From antiquity to present days
  • Marco AielloAffiliated withUniversity of Groningen Email author 
  • , Guram BezhanishviliAffiliated withNew Mexico State University
  • , Isabelle BlochAffiliated withTelecom ParisTech (ENST), CNRS UMR 5141 LTCI
  • , Valentin GorankoAffiliated withTechnical University of Denmark


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.


Modal logic Geometry Topology Mathematical morphology