A FORMAL APPROACH TO TWO-DIMENSIONAL TEMPORAL DATABASES By SEUNG-KYUM KIM A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA

of Thesis Presented to the Graduate School of the University of Florida in Partial Ful llment of the Requirements for the Degree of Master of Science A FORMAL APPROACH TO TWO-DIMENSIONAL TEMPORAL DATABASES By Seung-Kyum Kim May, 1993 Chairman: Dr. Sharma Chakravarthy Major Department: Computer and Information Sciences In this thesis, we propose a formal de nition of temporal validity, which we believe is the rst and the most comprehensive quanti cation of that notion. The temporal validity is developed into the notion of sort of validity. With the sort of validity, we can dispel the confusion among various time concepts introduced for temporal databases. Further, we discuss the problem of preserving multiple past states of a temporal database, which leads to the identi cation of a maximal set of time concepts and multidimensional representations. It is shown that the time concept, event time is needed to properly model retroactive and proactive updates, as it is not possible to model them using the valid and transaction times as thought earlier. Then, we extend the one-dimensional temporal validity into a two-dimensional one and introduce the notion of valid pattern. Based on the valid pattern, the notion ofmultihistory is developed, which precisely models the evolution of data object along two-dimensional time. We show that the notion of multihistory is easily implemented viii upon the relational data model by the attribute time-stamping. We also introduce the bipolar time-stamping as a two-dimensional attribute time-stamping, in addition to the usual, rectangular time-stamping.