Tuple calculus: Formal definition and conversion from first-order calculus

In classical database theory, relational calculus has long been used in expressing query formulae and integrity constraints. In fact, relational calculus formulae are much easier to deal with than first-order formulae when evaluating queries and validating database updates in the database environment. In deductive databases, however, first-order calculus is preferred because it is convenient when proof procedures are involved. Since both situations should coexist in advanced information systems, it is very desirable to devise a conversion procedure between relational calculus and first-order calculus. In this paper, interpretation of first-order formulae in the database environment is discussed first, then tuple calculus, an extension of relational calculus, is presented. This extension enables us to describe query formulae and general rules necessary in advanced information systems, in particular, dealing with complex objects. Finally, a conversion algorithm from first-order formulae into tuple calculus formulae is presented. Several application issues are also included.