Relation algebras of Sugihara, Belnap, Meyer, and Church

Algebras introduced by, or attributed to, Sugihara, Belnap, Meyer, and Church are representable as algebras of binary relations with set-theoretically defined operations. They are definitional reducts or subreducts of proper relation algebras. The representability of Sugihara matrices yields sound a...

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Bibliographic Details
Published inJournal of logical and algebraic methods in programming Vol. 117; p. 100604
Main Authors Kramer, R.L., Maddux, R.D.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2020
Subjects
Crystal lattice
Definitional reduct
Proper relation algebras
R-mingle
Relevance logic
Sugihara matrices
Sugihara matrices
Relevance logic
Crystal lattice
R-mingle
Definitional reduct
Proper relation algebras
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Summary:Algebras introduced by, or attributed to, Sugihara, Belnap, Meyer, and Church are representable as algebras of binary relations with set-theoretically defined operations. They are definitional reducts or subreducts of proper relation algebras. The representability of Sugihara matrices yields sound and complete set-theoretical semantics for R-mingle.
ISSN:2352-2208
DOI:10.1016/j.jlamp.2020.100604