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Algebra Logika, 2016, Volume 55, Number 3, Pages 273–299 (Mi al742)  

This article is cited in 4 scientific papers (total in 4 papers)

Dynamic mereotopology. III. Whiteheadian type of integrated point-free theories of space and time. III

D. Vakarelov

Sofia University, Faculty of mathematics and informatics, Department of mathematical logic and applications, Blvd James Bourchier 5, Sofia, Bulgaria

Abstract: This is the third in a three-part series of papers shortly denoted by Part I [Algebra i Logika, 53, No. 3 (2014), 300–322], Part II [Algebra i Logika, 55, No. 1 (2016), 14–36], and Part III. The papers mentioned are devoted to some Whiteheadean theories of space and time. Part I contains a historical introduction and some facts from static mereotopology. Part II introduces a point-based definition of a dynamic model of space and the definition of a standard dynamic contact algebra based on the so-called snapshot construction. The given 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. In Part II, a number of statements for these relations are proven, which in the present 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. Part III deals with a representation theory for dynamic contact algebras, and the main theorem says that each dynamic contact algebra in some natural class is representable as a standard dynamic contact algebra in the same class.

Keywords: dynamic contact algebra, dynamic mereotopology, point-free theory of space and time, representation theorems.

DOI: https://doi.org/10.17377/alglog.2016.55.301

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English version:
Algebra and Logic, 2016, 55:3, 181–197

Bibliographic databases:

UDC: 510.65
Received: 01.11.2013

Citation: D. Vakarelov, “Dynamic mereotopology. III. Whiteheadian type of integrated point-free theories of space and time. III”, Algebra Logika, 55:3 (2016), 273–299; Algebra and Logic, 55:3 (2016), 181–197

Citation in format AMSBIB
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\paper Dynamic mereotopology.~III. Whiteheadian type of integrated point-free theories of space and time.~III
\jour Algebra Logika
\yr 2016
\vol 55
\issue 3
\pages 273--299
\mathnet{http://mi.mathnet.ru/al742}
\crossref{https://doi.org/10.17377/alglog.2016.55.301}
\transl
\jour Algebra and Logic
\yr 2016
\vol 55
\issue 3
\pages 181--197
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. Vakarelov, “Actual existence predicate in mereology and mereotopology”, Rough Sets, IJCRS 2017, v. II, Lecture Notes in Artificial Intelligence, 10314, eds. L. Polkowski, Y. Yao, P. Artiemjew, D. Ciucci, D. Liu, D. Slezak, B. Zielosko, Springler, 2017, 138–157  crossref  isi  scopus
    2. D. Vakarelov, “Mereotopologies with predicates of actual existence and actual contact”, Fundam. Inform., 156:3-4 (2017), 413–432  crossref  mathscinet  zmath  isi  scopus
    3. P. Dimitrov, D. Vakarelov, “Dynamic contact algebras and quantifier-free logics for space and time”, Sib. elektron. matem. izv., 15 (2018), 1103–1144  mathnet  crossref
    4. D. Vakarelov, “Point-free theories of space and time”, J. Appl. Log.-IFCOLOG, 7:6 (2020), 1243–1321  isi
  • Алгебра и логика Algebra and Logic
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