MATCHING FUNCTIONS AND DISAGGREGATIONS IN DATABASES

A new algebraic operator, called matching function, is introduced. The composition of matching functions and cartesian products, named an MC-mapping, is then studied. It is shown that the set of all MC-mappings generates the well-known conjunctive queries without constant. A simple algebraic axiomatisation is given for proving containment (and thus equality) between MC-mappings. MC-dependencies are defined as containment between two MC-mappings and shown to be equivalent to non-typed embedded implicational dependencies.

Another algebraic operator, called (X-)disaggregation, which is an inverse of the aggregation described by Smith and Smith, is also introduced. Some general properties of (X-) disaggregation, as well as the closure of particular dependency families under (X-) disaggregation, are investigated. Finally, the closure of free families under matching function, cartesian product, selection and disaggregation, and under subsets of these four operations, is studied. In particular, some special families, i.e., functional dependency families, one-join dependency families and "simple" families, are characterized in terms of closure of free families under some of these operations.