An extension of the relational data model to incorporate ordered domains

Abstract

We extend the relational data model to incorporate partial orderings into data domains, which we call the ordered relational model. Within the extended model, we define the partially ordered relational algebra (the PORA) by allowing the ordering predicate ⊑ to be used in formulae of the selection operator (σ). The PORA expresses exactly the set of all possible relations that are invariant under order-preserving automorphism of databases. This result characterizes the expressiveness of the PORA and justifies the development of Ordered SQL (OSQL) as a query language for ordered databases. OSQL provides users with the capability of capturing the semantics of ordered data in many advanced applications, such as those having temporal or incomplete information. Ordered functional dependencies (OFDs) on ordered databases are studied, based on two possible extensions of domain orderings: pointwise ordering and lexicographical ordering. We present a sound and complete axiom system for OFDs in the first case and establish a set of sound and complete chase rules for OFDs in the second. Our results suggest that the implication problems for both cases of OFDs are decidable and that the enforcement of OFDs in ordered relations are practically feasible. In a wider perspective, the proposed model explores an important area of object-relational databases, since ordered domains can be viewed as a general kind of data type.