Dynamic Mereotopology. III. Whiteheadian Type of Integrated Point-Free Theories of Space and Time. II

Abstract

This is the second in a three-part series of papers shortly denoted by Part I [1], and Part III (Algebra and Logic, 55, No. 3). The papers mentioned are devoted to some Whiteheadian theories of space and time. Part I contains a historical introduction and some facts from static mereotopology. The present Part II introduces a point-based definition of dynamic model of space and standard dynamic contact algebra based on the so-called snapshot construction. This model has an explicit time structure with an explicit set of time points equipped with a before-after relation and a set of regions changing in time, called dynamic regions. The dynamic model of space contains several definable spatio-temporal relations between dynamic regions: space contact, time contact, precedence, and some others. We prove a number of statements for these relations, which in Part III are taken as axioms for the abstract definition of some natural classes of dynamic contact algebras, considered as an algebraic formalization of dynamic mereotopology.