The relational model of data and cylindric algebras

摘要

It is shown how the theory of cylindric algebras (a notion introduced by Tarski and others as a tool in the algebraization of the first order predicate calculus) can give a new insight into Codd's relational model of data. The relational algebra of Codd can be embedded in a natural way into a cylindric algebra where the join operation becomes the usual set-theoretical intersection. It is shown, by using known facts from the theory of cylindric algebras, that a version of the relational algebra is not finitely axiomatizable and that the equivalence problem for certain relational expressions is undecidable. A duality between the project-join and selectunion operator pairs is also briefly discussed.