Codd table representations under weak possible world semantics

Abstract

Abstract. Codd tables are databases that can carry Codd’s null “value unknown at present ” in columns that are specified as NULL. Under Lev-ene and Loizou’s possible world semantics we investigate the combined class of uniqueness constraints and functional dependencies over Codd tables. We characterize the implication problem of this class axiomati-cally, logically and algorithmically. Since the interaction of members in this class is intricate data engineers can benefit from concise sample ta-bles. Therefore, we investigate structural and computational properties of Armstrong tables. These are Codd tables that satisfy the consequences of a given set of elements in our class and violate all those elements that are not consequences. We characterize when a given Codd table is an Armstrong table for any given set of our class. From this result we es-tablish an algorithm that computes an Armstrong table in time that is at most quadratic in the number of rows in a minimum-sized Armstrong table. Data engineers can use our Armstrong tables to judge, justify, convey and test their understanding of the application domain.