In a relational database, NULL values within a key are usually disallowed which is called the "entity integrity rule". However, it can be shown that for keys consisting of more than one attribute NULL values can be allowed as long as no duplicates can occur by any replacement of NULL by a proper value. This, in turn, requires that the key tuples containing NULL values are "pairwise incompatible" which means that they differ in at least one proper value. In order to gain such sets of key tuples, maximal sets of pairwise incompatible tuples are constructed for a given set of attributes; any set of key tuples with NULL values, then, is a subset of such a maximal set. These maximal sets, moreover, must cover every fully specified tuple having the attributes given, with a tuple containing NULL for some attribute covering all the tuples which are obtained when replacing NULL by every proper value for this attribute. Maximal sets in which every tuple contains at least one NULL value turn out to be of particular interest. Maximal sets of such tuples are constructed using the notion of "groups" of tuples, with a "group" consisting of tuples having NULL for a fixed set of attributes, and using the notion of attributes "distinguishing" between such groups. The cases of two and of three such distinguishing attributes are discussed in detail, each of these cases requiring separate study and, in particular for the case of three such attributes, some technical apparatus.     «

In a relational database, NULL values within a key are usually disallowed which is called the "entity integrity rule". However, it can be shown that for keys consisting of more than one attribute NULL values can be allowed as long as no duplicates can occur by any replacement of NULL by a proper value. This, in turn, requires that the key tuples containing NULL values are "pairwise incompatible" which means that they differ in at least one proper value. In order to gain such sets of key tuples,...    »