Some algebraic theory for many-valued relation algebras

Abstract.

We study MV-relation-algebras, appearing by abstracting away from the concrete many-valued relations and the operations on them, such as composition and converse. MV-relation-algebras are MV generalizations of the relation algebras developed by A. Tarski and his school starting from the late forties. Some facts about ideals, congruences, and various types of elements are proved. A characterization of the “natural” MV-relation-algebras (a parameterized analogue of the classical full proper relation algebras) is also provided, as well as a first-order elementary description of matrix MV-relation algebras.