Abstract
This paper addresses the mathematical relation on a set of periods and temporal indexing constructions as well as their applications. First we introduce two concepts, i.e. the temporal connection and temporal inclusion, which are equivalence relation and preorder relation respectively. Second, by studying some basic topics such as the division of “large” equivalence classes and the overlaps of preorder relational sets, we propose a temporal data index model (TDIM) with a tree-structure consisting of a root node, equivalence class nodes and linearly ordered branch nodes. Third, we study algorithms for the temporal querying and incremental updating as well as dynamical management within the framework of TDIM. Based on a proper mathematical supporting, TDIM can be applied to researching some significant practical cases such as temporal relational and temporal XML data and so on.
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