Information Dependencies

Abstract

This paper uses the tools of information theory to examine and reason about the information content of the attributes within a relation instance. For two sets of attributes, an information dependency measure (InD measure) characterizes the uncertainty remaining about the values for the second set when the values for the first set are known. A variety of arithmetic inequalities (InD) are shown to hold among InD measures; InD inequalities hold in any relation instance. Numeric constraints (InD) on InD measures, consistent with the InD inequalities, can be applied to relation instances. Remarkably, functional and multivalued dependencies correspond to setting certain constraints to zero, with Armstrong's axioms shown to be consequences of the arithmetic inequalities applied to constraints. As an analog of completeness, for any set of constraints consistent with the inequalities, we may construct a relation instance that approximates these constraints within any positive epsilon.