Positive Boolean Dependencies

Abstract The class of Boolean dependencies for a relational database corresponds under a natural interpretation to the family of all Boolean terms that can be formed using the attributes of the relational as variables. It is shown that the consequence relation for this class of dependencies is not the same as the consequence relation for proportional logic. However, if positive Boolean terms are considered only, then the two consequence relations are equivalent. Examples are given to illustrate how positive Boolean dependencies can be used to represent some familiar combinatorial objects.