Topological properties of spatial databases in the polynomial constraint model

During the last decade the number of computer applications which is used to store and manipulate spatial data has steadily increased. Kanellakis, Kuper and Revesz have introduced the very powerful and elegant polynomial constraint model for spatial databases. Various languages have been developed to query databases in this model like for instance the spatial calculus and extensions of it with recursion. An important class of queries are the topological queries. In this thesis we study topological properties of spatial databases in the polynomial constraint model. Firstly, we have studied topological elementary equivalence. We give a characterization of topological elementary equivalence of closed 2-dimensional databases in terms of a known topological property, namely that they are locally conical. Further, we study the topological properties that can be expressed in the spatial calculus. We propose a two-tiered logic of which we conjecture that it captures exactly the topological spatial calculus queries. We prove this conjecture in a number of special cases. We also study topological properties that are not expressible in the calculus, namely topological equivalence and topological connectivity. We show that topological equivalence is a decidable property of 2-dimensional spatial databases. We study the language spatial Datalog and its potential to express the topological connectivity test. We study termination condition of spatial Datalog programs and discuss a number of implementations of the connectivity test.