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Algebra Logika, 2016, Volume 55, Number 1, Pages 14–36 (Mi al727)  

This article is cited in 5 scientific papers (total in 5 papers)

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

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 second part from the series of papers shortly denoted by part I [Algebra i Logika, 53, No. 3 (2014), 300–322] and part III [Algebra i Logika, 55, No. 3]. These papers are devoted to some Whiteheadean theories of space and time. Part I contains a historical introduction and some facts from static mereotopology. The present part is devoted to the introduction of a point-based definition of dynamic model of space and standard dynamic contact algebra based on the so called snapshot construction. This model contains explicit time structure with 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 for these relations some statements, which in part III are taken as axioms for the abstract definition of some natural classes of dynamic contact algebras, considered as algebraic formulation of dynamic mereotopology.

Keywords: snapshot construction, point-based dynamic model of space, standard dynamic contact algebra.

DOI: https://doi.org/10.17377/alglog.2016.55.102

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English version:
Algebra and Logic, 2016, 55:1, 9–23

Bibliographic databases:

UDC: 510.65
Received: 01.11.2013

Citation: D. Vakarelov, “Dynamic mereotopology III. Whiteheadean type of integrated point-free theories of space and time. II”, Algebra Logika, 55:1 (2016), 14–36; Algebra and Logic, 55:1 (2016), 9–23

Citation in format AMSBIB
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\paper Dynamic mereotopology~III. Whiteheadean type of integrated point-free theories of space and time.~II
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\vol 55
\issue 1
\pages 14--36
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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, “Dynamic mereotopology. III. Whiteheadian type of integrated point-free theories of space and time. III”, Algebra and Logic, 55:3 (2016), 181–197  mathnet  crossref  crossref  isi
    2. D. Vakarelov, “Actual existence predicate in mereology and mereotopology”, Rough Sets, IJCRS 2017, v. II, Lecture Notes in Artificial Intelligence, 10314, ed. L. Polkowski, Y. Yao, P. Artiemjew, D. Ciucci, D. Liu, D. Slezak, B. Zielosko, Springler, 2017, 138–157  crossref  isi  scopus
    3. D. Vakarelov, “Mereotopologies with predicates of actual existence and actual contact”, Fundam. Inform., 156:3-4 (2017), 413–432  crossref  mathscinet  zmath  isi  scopus
    4. 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
    5. 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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