B. Kuijpers and J. Van den Bussche. On capturing first-order topological properties of planar spatial databases. In C. Beer/and P. Buneman, editors, ICDT'99: 7th International Conference on Database Theory, volume 1540 of Lecture Notes in ComputerScience, pages 187 198, Jerusalem, Israel, January 1999. Springer. Home/Search Document Details and Download
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An Ehrenfeucht-Fraïssé Game Approach to Collapse.. - Schweikard (Correct)
....gives a listing of recent papers in which the lifting method has been used: compl. dbs easy dbs result for result for easy dbs compl. dbs evaluation of evaluation of [29] planar spatial finite dbs fixpoint counting top. FO( dbs queries queries over collapse from collapse from [19] region dbs finite dbs gen.FO( q , x) top. FO( x) to FOadon( to top. FO( over over finitely logical character complexity of [15] representable finite dbs ization of complexity query evaluation dbs classes finitely natural generic natural generic [5] representable finite dbs ....
....query against the spatial database can be efficiently translated into a fixpoint counting query against the topological invariant. This shows that efficient query evaluation for the topological invariants leads to efficient query evaluation for spatial databases. Kuijpers and Van den Bussche [19] show that all topological FO( x) queries over socalled (fully 2D) region databases over can already be expressed in FO( A crucial step in their proof is to represent region databases by finite databases, to which the natural generic collapse of [6] applies, i.e. the collapse from ....
[Article contains additional citation context not shown here]
B. Kuijpers and J. Van den Bussche. On capturing first-order topological properties of planar spatial databases. In C. Beer/and P. Buneman, editors, ICDT'99: 7th International Conference on Database Theory, volume 1540 of Lecture Notes in ComputerScience, pages 187 198, Jerusalem, Israel, January 1999. Springer.
On First-Order Topological Queries - Grohe, Segoufin (2000) (Correct)
....various applications of spatial databases. For example, in geographical databases, queries like Is region A adjacent to region B , Is there a road from A to B , or Is A an island come up very naturally. Therefore, topological queries have received a lot of attention in the literature (e.g. [KPV97, PSV99, SV98, KV99]) A basic result known about topological queries is that connectivity of a region is not expressible in first order logic [GS99, GS97, BDLW96] Thinking of geographical databases again, planar (or 2dimensional) database instances, where all relations are embedded in the plane R 2 , are of ....
....in the finite case. KPV97] asked whether their results generalize to database instances with a region that is not necessarily closed; we give a negative answer to this question. For instances with one closed region that satisfy the additional technical condition of being fully two dimensional, [KV99] introduced a cone logic CL and proved that it is sound and complete for topological FO. They asked if their results generalize to instances with not necessarily closed regions or several regions, again we give a negative answer. KPV97] introduced two local operations on spatial database ....
[Article contains additional citation context not shown here]
Bart Kuijpers and Jan Van den Bussche. On capturing first-order topological properties of planar spatial databases. In Proc. of Intl. Conf. on Database Theory, pages 187--198, 1999.
On First-Order Topological Queries - Grohe, Segoufin (Correct)
....various applications of spatial databases. For example, in geographical databases, queries like Is region A adjacent to region B , Is there a road from A to B , or Is A an island come up very naturally. Therefore, topological queries have received a lot of attention in the literature (e.g. [KPV97, PSV99, SV98, KV99]) A basic result known about topological queries is that connectivity of a region is not expressible in first order logic [GS99, GS97, BDLW96] Thinking of geographical databases again, planar (or 2dimensional) database instances, where all relations are embedded in the plane R 2 , are of ....
....in the finite case. KPV97] asked whether their results generalize to database instances with a region that is not necessarily closed; we give a negative answer to this question. For instances with one closed region that satisfy the additional technical condition of being fully two dimensional, [KV99] introduced a cone logic CL and proved that it is sound and complete for topological FO. They asked if their results generalize to instances with not necessarily closed regions or several regions, again we give a negative answer. KPV97] introduced two local operations on spatial database ....
[Article contains additional citation context not shown here]
Bart Kuijpers and Jan Van den Bussche. On capturing first-order topological properties of planar spatial databases. In Proc. of Intl. Conf. on Database Theory, pages 187--198, 1999.
Reachability and Connectivity Queries in Constraint.. - Benedikt, Grohe.. (1999) (5 citations) (Correct)
....that is absent from first order constraint query languages, there are many other geometric properties which are conceptually (and even algorithmically) simple that are inexpressible as well: the query asking whether a planar region is simply connected, to take just one example. In fact, results of [20, 22] show, roughly, that the only purely topological facts of a single region expressible in first order queries are local they merely assert the existence or nonexistence of points with a given topological type. In this paper, we consider extensions of first order constraint query languages ....
.... language was given for linear constraints [15] Besides, this approach can only work for those queries applied as top level operators (i.e. outputs cannot be reused by other queries) There exists extensive literature on first order definable topological properties of constraint databases [26, 20, 22, 30] and it is well known that connectivity and reachability are not first order [4] Our results on application to hybrid systems are directly inspired by [24, 25] Organization We introduce notations in Section 2. In Section 3, we deal with closure under topological properties. We first prove a ....
B. Kuijpers and J. Van den Bussche. On capturing firstorder topological properties of planar spatial databases. In ICDT'99, pages 187--198.
Reachability and Connectivity Queries in Constraint.. - Benedikt, Grohe.. (1999) (5 citations) (Correct)
....that is absent from first order constraint query languages, there are many other geometric properties which are conceptually (and even algorithmically) simple that are inexpressible as well: the query asking whether a planar region is simply connected, to take just one example. In fact, results of [20, 22] show, roughly, that the only purely topological facts of a single region expressible in first order queries are local they merely assert the existence or nonexistence of points with a given topological type. In this paper, we consider extensions of first order constraint query languages ....
.... language was given for linear constraints [15] Besides, this approach can only work for those queries applied as top level operators (i.e. outputs cannot be reused by other queries) There exists extensive literature on first order definable topological properties of constraint databases [26, 20, 22, 31] which connectivity and reachability are not first order. Our results on application to hybrid systems are directly inspired by [24, 25] Organization We introduce notations in Section 2. In Section 3, we deal with closure under topological properties. We first prove a number of general ....
B. Kuijpers and J. Van den Bussche. On capturing first-order topological properties of planar spatial databases. In ICDT'99, pages 187--198.
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