Set-theoretic problems of null completion in relational databases
Arthur M. Keller · Information Processing Letters · 1986
When considering using databases to represent incomplete information, the relationship between two facts where one may imply the other needs to be addressed. In relational databases, this question becomes whether null completion is assumed. That is, does a (possibly partially-defined) tuple imply the existence of tuples that are ‘less informative’ than the original tuple. We show that no relational algebra, that assumes equivalence under null completion, can include set-theoretic operators that are compatible with ordinary set theory. Thus, the approach of x-relations is incompatible with the axioms of a boolean algebra.