Dynamic Mereotopology. III. Whiteheadean Type of Integrated Point-Free Theories of Space and Time. I

作者：Vakarelov D^*

来源：Algebra and Logic, 2014, 53(3): 191-205.

DOI：10.1007/s10469-014-9283-8

• Whiteheadean type theory
• dynamic mereotopology
• point-free theory of space and time

Some Whiteheadean type point-free theories of space and time are presented. Here the term %26quot;point-free%26quot; means that neither space points nor time moments are assumed as primitives. The theory has an algebraic formulation, called dynamic contact algebra (DCA), which is a Boolean algebra whose elements symbolize dynamic regions changing in time, with several spatio-temporal relations between the regions: space contact, time contact, preceding, and some others. In the second part of the paper, a class of intended standard models of DCAs of topological kind will be introduced, which is a reason for calling DCAs dynamic mereotopologies. The main result of the paper is a kind of representation theorem saying that each DCA in a given class of DCAs is isomorphic to some DCA of standard type in the same class (see the third part of the paper). The first part contains a historical introduction and some facts on static mereotopology needed in succeeding parts-namely, the definitions of contact and precontact algebras, their models and representation theory.

• 出版日期2014-7