Extending Functional Dependencies in Indefinite Sequence Relations

Abstract

We introduce the concept of an indefinite sequence relation r over a relation schema R in order to capture the semantics of sequence data having indefinite values. Indefinite information may arise in a relation containing data from a mobile environment or from a multi-database system. An indefinite tuple allows an attribute value to contain a set of values, which can be employed to represent disjunction of information. A definite sequence relation extracted from r, while maintaining its ordering, has all indefinite cells replaced with just one of the indefinite values. We establish a formal hierarchical structure over the class of indefinite sequence relations having a fixed schema and cardinality, which can be employed to classify the relations into different levels of precision. A functional dependency (FD) ƒ satisfies in r if there is a definite sequence relation over R, extracted from r, that satisfies ƒ as the same way a conventional relation does. Our main result shows that FDs in this context have the following two important features. First, Lien and Atzeni’s axiom system [23,3] for FDs in incomplete relations, rather than the well-known Armstrong’s axiom system, is sound and complete for FDs in indefinite sequence relations. It implies that the established results for FDs in incomplete relations, such as the closure and implication algorithms, can be extended to FDs in indefinite sequence relations. Second, the satisfaction for FDs is non-additive, meaning that in a given relation the satisfaction of each ƒ in F may not lead to the the satisfaction of F.