Lexicographically ordered functional dependencies and their application to temporal relations

Proposes an ordered relational model and defines lexicographically ordered functional dependencies (LOFDs) according to the lexicographical ordering on the Cartesian product of those domains associated with the involved attributes. An LOFD in the ordered relational model captures the semantics of a monotonicity property between two sets of data. We establish a set of sound and complete chase rules for LOFDs and show that the implication problem for LOFDs is decidable. Defining temporal relations as a special case of linearly ordered relations over schemas consisting of time, time-variant and time-invariant attributes, we demonstrate that LOFDs are a useful semantic constraint which can be employed to maintain the consistency between the time data in different time measurement systems. We also formally define temporal functional dependencies (TFDs) in order to express the semantics of the temporally ordered data. A TFD can be expressed in terms of a set of LOFDs in which every element has a sequence of time attributes on its left-hand side and a single time-variant attribute on its right-hand side. Finally, we exhibit a sound and complete axiom system for TFDs.