An Expressive Language for Linear Spatial Database Queries.

Luc Vandeurzen, Marc Gyssens, Dirk Van Gucht: An Expressive Language for Linear Spatial Database Queries. PODS 1998: 109-118

@inproceedings{DBLP:conf/pods/VandeurzenGG98,
  author    = {Luc Vandeurzen and
               Marc Gyssens and
               Dirk Van Gucht},
  title     = {An Expressive Language for Linear Spatial Database Queries},
  booktitle = {Proceedings of the Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium
               on Principles of Database Systems, June 1-3, 1998, Seattle, Washington},
  publisher = {ACM Press},
  year      = {1998},
  isbn      = {0-89791-996-3},
  pages     = {109-118},
  ee        = {http://doi.acm.org/10.1145/275487.275500, db/conf/pods/VandeurzenGG98.html},
  crossref  = {DBLP:conf/pods/98},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

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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Proceedings of the Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, June 1-3, 1998, Seattle, Washington. ACM Press 1998, ISBN 0-89791-996-3
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References

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