| Existing data models and design principles for temporal databases are based on the assumption that a temporal data is associated with an interval as well as its sub-intervals. This type of temporal data is called homogeneous data. A temporal data which is associated with an interval, but not its sub-intervals, is called a non-homogeneous data. Existing data models cannot capture non-homogeneous data accurately, and the existing design principles are not applicable in temporal databases that contain non-homogeneous data. In this dissertation, the relational data model is extended to support both homogeneous and non-homogeneous data. A design principle which avoids inconsistency in temporal databases, that contain homogeneous data as well as non-homogeneous data, is studied.; In the proposed extension of the relational data model, temporal relations are classified into two types; property relations and representative relations. A tuple in a property relation is associated with the valid time and its sub-intervals, while a tuple in a representative relation is associated with only the whole interval of its valid time. Thus, the valid time in a property relation is decomposable, but the valid time in a representative relation is not. Based on this characteristics, the valid time in a property relation and that in a representative relation cannot be used in the same manner. In the extension of relational algebra for temporal relations, the calculation of the valid time in a relation, created by relational operators, is determined by the types of the temporal relations. Thus, it guarantees proper use of the valid time.; A type of inconsistency, called P-inconsistency, can occur in temporal databases with homogeneous and non-homogeneous data. A normal form, called P-consistency Normal Form (PCNF), which avoids P-inconsistency, is proposed in this dissertation. PCNF is based on types of attributes, functional dependencies, and property dependencies (P-dependencies), in temporal relations. A normalization algorithm for PCNF is presented. However, it does not always give the minimum number of normalized relations. We prove that finding a decomposition that gives the minimum number of normalized relations is an NP-complete problem. We have also proven that the problem of finding equivalent sets of attributes under a set of dependencies is an NP-complete problem. This problem is a more general problem, and is the basis of the proof that finding a decomposition that gives the minimum number of normalized relations is an NP-complete problem. Finally, a heuristic that gives a minimum number of normalized relations is provided. |
