The characterization of branching dependencies

A new type of dependencies in a relational database model is introduced. If b is an attribute, A is a set of attributes then it is said that -depends on A, in notation , in a database r if there are no rows in r such that they have at most p different values in A, but different values in b. -dependency is the classical functional dependency. Let (A) denote the set . The set function (A) is characterized if . Implications among -dependencies are also determined.