Stell, JG (2015) Symmetric Heyting relation algebras with applications to hypergraphs. Journal of Logical and Algebraic Methods in Programming, 84 (3). pp. 440-455. ISSN 2352-2208
Abstract
A relation on a hypergraph is a binary relation on the set consisting of all the nodes and the edges, and which satisfies a constraint involving the incidence structure of the hypergraph. These relations correspond to join preserving mappings on the lattice of sub-hypergraphs. This paper introduces a generalization of a relation algebra in which the Boolean algebra part is replaced by a Heyting algebra that supports an order-reversing involution. A general construction for these symmetric Heyting relation algebras is given which includes as a special case the algebra of relations on a hypergraph. A particular feature of symmetric Heyting relation algebras is that instead of an involutory converse operation they possess both a left converse and a right converse which form an adjoint pair of operations. Properties of the converses are established and used to derive a generalization of the well-known connection between converse, complement, erosion and dilation in mathematical morphology. This provides part of the foundation necessary to develop mathematical morphology on hypergraphs based on relations on hypergraphs.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2014, Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Logical and Algebraic Methods in Programming. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Logical and Algebraic Methods in Programming, (2014) DOI 10.1016/j.jlamp.2014.12.001 |
Keywords: | Relation algebra; symmetric Heyting algebra,; hypergraph; mathematical morphology; left converse; right converse |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 04 Feb 2015 14:56 |
Last Modified: | 03 Dec 2020 18:21 |
Published Version: | http://dx.doi.org/10.1016/j.jlamp.2014.12.001 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jlamp.2014.12.001 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:82604 |