Dynamic Mereotopology II: Axiomatizing some Whiteheadean Type Space-time Logics
نویسنده
چکیده
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.
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