A foundation of CODD's relational maybe-operations

Abstract

Database relations which possibly contain maybe-tuples and null values of type “value at present unknown” are studied. Maybe-tuples and null values are formally interpreted by our notion of representation , which uses classical notions of predicate logic, elaborates Codd's proposal of maybe-tuples, and adopts Reiter's concept of a closed world. Precise notions of information content and redundancy , associated with our notion of representation, are investigated. Extensions of the relational algebra to relations with maybe-tuples and null values are proposed. Our extensions are essentially Codd's, with some modifications. It is proved that these extensions have natural properties which are formally stated as being adequate and restricted . By the treatment of difference and division, our formal framework can be used even for operations that require “negative information.” Finally, extensions of update operations are discussed.