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- W2127691971 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." @default.
- W2127691971 created "2016-06-24" @default.
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- W2127691971 date "2015-05-01" @default.
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- W2127691971 title "Symmetric Heyting relation algebras with applications to hypergraphs" @default.
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- W2127691971 doi "https://doi.org/10.1016/j.jlamp.2014.12.001" @default.
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