The implication and finite implication problems for typed template dependencies (Q1071525)

The class of typed template dependencies is a class of data dependencies that includes embedded multivalued and join dependencies. It is shown that the implication and the finite implication problems for this class are unsolvable. An immediate corollary is that this class has no formal system for finite implication. It is also shown how to construct a finite set of typed template dependencies whose implication and finite implication problems are unsolvable. The class of projected join dependencies is a proper subclass of the above class, and it generalizes slightly embedded join dependencies. It is shown that the implication and the finite implication problems for this class are also unsolvable. An immediate corollary is that this class has no universe-bounded formal system for either implication or finite implication.