The purpose of good database logical design is to eliminate data redundancy and insertion and deletion anomalies. In order to achieve this objective for temporal databases, the notions of temporal types, which formalize time granularities, and temporal functional dependencies (TFDs) are introduced. A temporal type is a monotonic mapping from ticks of time (represented by positive integers) to time sets (represented by subsets of reaIs) and is used to capture various standard and user-defined calendars. A TFD is a proper extension of the traditional functional dependency and takes the form X -->(mu) Y, meaning that there is a unique value for Y during one tick of the temporal type mu for one particular X value. An axiomatization for TFDs is given. Because a finite set of TFDs usually implies an infinite number of TFDs, we introduce the notion of and give an axiomatization for a finite closure to effectively capture a finite set of implied TFDs that are essential to the logical design. Temporal normalization procedures with respect to TFDs are given. Specifically, temporal Boyce-Codd normal form (TBCNF) that avoids all data redundancies due to TFDs, and temporal third normal form (T3NF) that allows dependency preservation, are defined. Both normal forms are proper extensions of their traditional counterparts, BCNF and 3NF. Decomposition algorithms are presented that give lossless TBCNF decompositions and lossless, dependency-preserving, T3NF decompositions.
