Order dependency in the relational model

AbstractThe relational model is formally extended to include fixed orderings on attribute domains. A new constraint, called order dependency, is then introduced to incorporate semantic information involving these orderings. It is shown that this constraint can be applied to enhance the efficiency of an implemented database. The thrust of the paper is to study logical implication for order dependency. The main theoretical results consist in (i) introducing a formalism analogous to propositional calculus for analyzing order dependency, (ii) exhibiting a sound and complete set of inference rules for order dependency, and (iii) demonstrating that determining logical implication for order dependency is co-NP-complete. It is also shown that there are sets of order dependencies for which no Armstrong relations exist