Ordered functional dependencies in relational databases

摘要

We extend the relational data model to incorporate linear orderings into data domains, which we call the ordered relational model. The conventional Functional Dependencies (FDs) are examined in the context of ordered relational databases by using the notion of System Ordering Independence (SOI), which refers to the desirable scenario that the ordering of tuples in a relation is independent of the implementation of the underlying DBMS. We also extend Armstrong's axiom system for FDs to object relations, which are a subclass of ordered relations that allow us to view tuples as objects. We formally define Ordered Functional Dependencies (OFDs) for the extended model by means of two possible extensions of domains, pointwise-orderings and lexicographical orderings. We first present a sound and complete axiom system for OFDs in the case of pointwise-orderings and then establish a sound and complete set of chase rules for OFDs in the case of lexicographical orderings. Our main result shows that the implication problems for both cases of OFDs are decidable, and that it is linear time for the case of pointwise-orderings.