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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2018, Volume 15, Pages 1103–1144
DOI: https://doi.org/10.17377/semi.2018.15.092
(Mi semr983)
 

This article is cited in 1 scientific paper (total in 1 paper)

Mathematical logic, algebra and number theory

Dynamic contact algebras and quantifier-free logics for space and time

P. Dimitrov, D. Vakarelov

Sofia University, Faculty of mathematics and informatics Department of mathematical logic and applications, Blvd James Bourchier 5, Sofia, Bulgaria
Full-text PDF (309 kB) Citations (1)
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Abstract: The paper is in the field of Region Based Theory of Space (RBTS), sometimes called mereotopology. RBTS is a kind of point-free theory of space based on the notion of region. Its origin goes back to some ideas of Whitehead, De Laguna and Tarski to build the theory of space without the use of the notion of point. Contact algebras present an algebraic formulation of RBTS and in fact give axiomatizations of the Boolean algebras of regular closed sets of some classes of topological spaces with an additional relation of contact. Dynamic contact algebras (DCA), are generalizations of contact algebras studying regions changing in time and present formal explications of Whitehead's ideas of integrated point-free theory of space and time. In the present paper we propose several new types of dynamic contact algebras and quantifier-free logics based on them. The logics are finitary, based on Modus Ponens and some nonstandard inference rules which replace the non-universal axioms of the corresponding DCA. In fact these logics can be considered as axiomatizations of the universal fragment of the first-order theory of the corresponding DCA. They can be treated as kinds of non-standard temporal logics for spatial regions changing in time. The difference with standard temporal logic is that we do not use temporal operators but temporal predicates. We present also snapshot semantics and Kripke style relational semantics for some of these logics, based on relational models for the corresponding DCA. The relational semantics helps to use some techniques adapted from modal logic to study some metalogical properties of the studied systems.
Keywords: region-based theory of space and time, contact algebra, dynamic contact algebra, representation theorem, quantifier-free first-order theory, rule-elimination theorem, non-standard temporal logic.
Funding agency Grant number
Bulgarian National Science Fund
This research is partially sponsored by contract with Bulgarian NSF, project title ``Space, Time and Modality: Relational, Algebraic and topological Models”.
Received September 25, 2018, published October 9, 2018
Bibliographic databases:
Document Type: Article
UDC: 510.2, 510.6
MSC: 03B60, 03G25
Language: English
Citation: P. Dimitrov, D. Vakarelov, “Dynamic contact algebras and quantifier-free logics for space and time”, Sib. Èlektron. Mat. Izv., 15 (2018), 1103–1144
Citation in format AMSBIB
\Bibitem{DimVak18}
\by P.~Dimitrov, D.~Vakarelov
\paper Dynamic contact algebras and quantifier-free logics for space and time
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1103--1144
\mathnet{http://mi.mathnet.ru/semr983}
\crossref{https://doi.org/10.17377/semi.2018.15.092}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000454860200034}
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  • https://www.mathnet.ru/eng/semr983
  • https://www.mathnet.ru/eng/semr/v15/p1103
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Full-text PDF :30
    References:34
     
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