Logic for physical space

Marco Aiello

Guram Bezhanishvili

Isabelle Bloch

Valentin Goranko

pp. 619-632

in: Sonja Smets, Johan van Benthem (eds), Logic meets physics, Synthese 186 (3), 2012.

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.