Breaking the Atom with Samson

The dependence atom =(x, y) was introduced in [11]. Here x and y are finite sets of attributes (or variables) and the intuitive meaning of =(x, y) is that the attributes x completely (functionally) determine the attributes y. One may wonder, whether the dependence atom is truly an atom or whether it has further constituents. My very pleasant co-operation with Samson Abramsky led to the breaking of this atom, with hitherto unforeseen consequences. Here is the story. A reasonable goal in logic is to capture the intuitive meaning of some concept by means of simple axioms. In the case of dependence atoms such simple axioms are the so-called Armstrong’s Axioms: