Dynamic mereotopology.~III. Whiteheadean type of integrated point-free theories of space and time.~I

D. Vakarelov

Algebra i logika, Tome 53 (2014) no. 3, pp. 300-322.

Résumé

Some Whiteheadean type point-free theories of space and time are presented. Here the term point-free 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 spatiotemporal relations between the regions: space contact, time contact, preceding, and some others. In the second part of the work, 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 work). 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.

Détail

Keywords: Whiteheadean type theory, dynamic mereotopology, pointfree theory of space and time.

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