ABSTRACT: In the near future, we can expect a great variety of languages to be proposed for interrogating and updating data bases. This paper attempts to provide a theoretical basis which may be used to determine how complete a selection capability is provided in a proposed data sublanguage independently of any host language in which the sublanguage may be embedded. A relational algebra and a relational calculus are defined. Then, an algorithm is presented for reducing an arbitrary relation-defining expression (based on the calculus) into a semantically equivalent expression of the relational algebra. Finally, some opinions are stated regarding the relative merits of calculus-oriented versus algebra-oriented data sublanguages from the standpoint of optimal search and highly discriminating authorization schemes.