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Title: An Expressive Language for Linear Spatial Database Queries
Authors: VANDEURZEN, Luc 
Van Gucht, Dirk
Issue Date: 1998
Publisher: Association for Computing Machinery
Source: Proceedings of the Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, June 1-3, 1998, Seattle, Washington, Pag. 109-118
Abstract: We exhibit a coordinate-based language, called PFOL, which is sound for the linear queries computable in first-order logic over the reals and extends the latter's restriction to linear arithmetic. To evaluate its expressive power, we first consider PFOL-fin, the PFOL queries that compute finite outputs upon finite inputs. In order to study this fragment of PFOL, we also define a syntactical language, called SPFOL, which is safe with respect to queries from finite inputs to finite outputs. We show that SPFOL has the same expressive power as SafeEuQl [15], whence all ruler-and-compass constructions in the plane on finite sets of points can be expressed in SPFOL. This result gives a geometrical justification of SPFOL, and highlights the richness of PFOL-fin. Then, we define finite representations for arbitrary semi-linear sets and show that there are PFOL programs for both the encoding and the decoding. This result is used (i) to identify a broad, natural class of linear queries expressible in PFOL, highlighting the richness of general PFOL, and (ii) to establish a general theorem about lifting query languages on finite databases to query languages on arbitrary linear databases. This theorem is applied to a recent result of Benedikt and Libkin [5] from finite to arbitrary semi-linear sets, yielding the existence of a natural, syntactically definable fragment of FO+poly sound and complete for all FO+poly-expressible linear queries.
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ISBN: 0-89791-996-3
Type: Proceedings Paper
Appears in Collections:Research publications

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