Relation algebras of Sugihara, Belnap, Meyer, and Church

Abstract

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.

39 pages, 6 tables, 5 figures, submitted to Journal of Logical and Algebraic Methods in Programming, third version, math-LO