Dynamic Mereotopology II: Axiomatizing some Whiteheadean Type Space-time Logics.
Dimiter Vakarelov · 2012
In this paper we present an Whiteheadean style point-free theory of space and time. Here ”point-free ” means that neither space points, nor time moments are assumed as primitives. The algebraic formulation of the theory, called dynamic contact algebra (DCA), is a Boolean algebra whose elements symbolize dynamic regions changing in time. It has three spatio-temporal relations between dynamic regions: space contact, time contact and preceding. We prove a representation theorem for DCA-s of topological type, reflecting the dynamic nature of regions, which is a reason to call DCA-s dynamic mereotopoly. We also present several complete quantifier-free logics based on the language of DCA-s.