Relational Representation Theorems for Extended Contact Algebras

In topological spaces, the relation of extended contact is a ternary relation that holds between regular closed subsets A , B and D if the intersection of A and B is included in D . The algebraic counterpart of this mereotopological relation is the notion of extended contact algebra which is a Boole...

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Bibliographic Details
Published inStudia logica Vol. 109; no. 4; pp. 701 - 723
Main Authors Balbiani, Philippe, Ivanova, Tatyana
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.08.2021
Springer Verlag (Germany)
Subjects
Computational Linguistics
Computer Science
Education
Logic
Logic in Computer Science
Mathematical Logic and Foundations
Philosophy
Point-free theory of space
Relational representation
Extended contact algebras
Mereotopology
Regular closed subsets
Contact algebras
Topological representation
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Summary:In topological spaces, the relation of extended contact is a ternary relation that holds between regular closed subsets A , B and D if the intersection of A and B is included in D . The algebraic counterpart of this mereotopological relation is the notion of extended contact algebra which is a Boolean algebra extended with a ternary relation. In this paper, we are interested in the relational representation theory for extended contact algebras. In this respect, we study the correspondences between point-free and point-based models of space in terms of extended contact. More precisely, we prove new representation theorems for extended contact algebras.
ISSN:0039-3215
1572-8730
DOI:10.1007/s11225-020-09923-0