Modelling and querying spatio-temporal data

Abstract

In this thesis, we started with defining spatio-temporal databases as a special type of constraint databases, meaning that we defined spatio-temporal objects to be semialgebraic subsets of (Rn × R). A consequence of this choice is that spatio-temporal data can be described by Boolean combinations of polynomial equations, which can be expressed in the language FO(+, ×, <, 0, 1). Although spatio-temporal databases have been studied for a decade already, the question “What are spatio-temporal database queries” is still actual. In relational database theory, it is common to require queries to be generic. A generic query asks only for properties that are shared by “isomorphic” encodings of the same data or, in other words, the result of a generic query depends only to a certain, limited extent on the actual internal representation of the database it is applied to. Chandra and Harel considered the permutations of the universal domain U of the database (that possibly fix some elements of the domain) as “isomorphisms” for relational databases. Paredaens, Van den Bussche and Van Gucht [58] have shown that for spatial databases, the definition of genericity is not unique and that it depends on the particular kind of geometry in which the spatial information is to be interpreted. Genericity of spatial databases hence is defined as a function of some group of geometric transformations....