Revisiting the Definition of the Relational Tuple Calculus

The tuple relational calculus has been based on the classical predicate logics. Databases are however not exactly representable in this calculus. They are finite. This finiteness results in a different semantics. The result of a query must be finite as well and must be based on the values in the database and in the query. In this case, negation and disjunction of query expression must be defined in a different way. The classical theory has developed restrictions to the tuple relational calculus such as safe formulas. This paper takes a different turn. We introduce a different definition of the tuple relational calculus and show that this calculus is equivalent to the relational algebra and thus equivalent to the safe tuple relational calculus.