License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2018.13
URN: urn:nbn:de:0030-drops-96805
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9680/
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Bonchi, Filippo ; Seeber, Jens ; Sobocinski, Pawel

Graphical Conjunctive Queries

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LIPIcs-CSL-2018-13.pdf (1 MB)

Abstract

The Calculus of Conjunctive Queries (CCQ) has foundational status in database theory. A celebrated theorem of Chandra and Merlin states that CCQ query inclusion is decidable. Its proof transforms logical formulas to graphs: each query has a natural model - a kind of graph - and query inclusion reduces to the existence of a graph homomorphism between natural models.
We introduce the diagrammatic language Graphical Conjunctive Queries (GCQ) and show that it has the same expressivity as CCQ. GCQ terms are string diagrams, and their algebraic structure allows us to derive a sound and complete axiomatisation of query inclusion, which turns out to be exactly Carboni and Walters' notion of cartesian bicategory of relations. Our completeness proof exploits the combinatorial nature of string diagrams as (certain cospans of) hypergraphs: Chandra and Merlin's insights inspire a theorem that relates such cospans with spans. Completeness and decidability of the (in)equational theory of GCQ follow as a corollary. Categorically speaking, our contribution is a model-theoretic completeness theorem of free cartesian bicategories (on a relational signature) for the category of sets and relations.

BibTeX - Entry

@InProceedings{bonchi_et_al:LIPIcs:2018:9680,
  author =	{Filippo Bonchi and Jens Seeber and Pawel Sobocinski},
  title =	{{Graphical Conjunctive Queries}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic  (CSL 2018)},
  pages =	{13:1--13:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Dan Ghica and Achim Jung},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9680},
  URN =		{urn:nbn:de:0030-drops-96805},
  doi =		{10.4230/LIPIcs.CSL.2018.13},
  annote =	{Keywords: conjunctive query inclusion, string diagrams, cartesian bicategories}
}

Keywords: conjunctive query inclusion, string diagrams, cartesian bicategories
Collection: 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)
Issue Date: 2018
Date of publication: 29.08.2018

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