DATA-TYPES OVER MULTIPLE-VALUED LOGICS

Let L be a multiple-valued logic. An equality-test algebra over L is a many-sorted algebra that contains the truth values of L in a special logic domain; it also includes certain operations that take values in the logic domain and are to be viewed as the characteristic functions of nonclassical predicates over the universe of the algebra. In particular the algebra contains for each sort s the characteristic function of the nonclassical equality predicate over the domain of sort s. Nonclassical data structures of this form arise naturally in various computer science contexts. The basic properties of nonclassical equality-test algebras are investigated, and an axiomatization of their conditional-equational theory is obtained for a large class of multiple-valued logics. Some consequences for the specification of nonclassical equality-test data types are drawn.