Logic for physical space From antiquity to present days Marco Aiello · Guram Bezhanishvili · Isabelle Bloch · Valentin Goranko

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.