Many-valued relation algebras (Q2577714)

Jónsson and Tarski introduced relation algebras in 1948 as algebraic models of binary relations. Relation algebras have a wide range of applications, ranging from the most abstract areas of mathematics to programming languages. To fix ideas, a concrete example of a relation algebra \(R\) is given by the totality of binary relations over a set \(X\) equipped with Boolean operations together with composition, converse and diagonal. A many-valued generalization of \(R\) is obtained by considering all \([0,1]\)-valued functions over the cartesian product \(X \times X\), with the appropriate MV-algebraic operations. The author considers more general structures, e.g., relation algebras based on Hájek's basic algebras, group relation algebras and ``complex'' algebras: the latter are a significant class of relation algebras, because every relation algebra is embeddable in a complex algebra. Various generalizations of the classical results on relation algebras are proved for these larger classes.