The University of Southampton
University of Southampton Institutional Repository

Graphical conjunctive queries

Graphical conjunctive queries
Graphical conjunctive queries
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.
Leibniz International Proceedings in Informatics (LIPIcs)
Bonchi, Filippo
3c53e89d-d280-4911-9938-eb861553d04e
Seeber, Jens
4c59db18-08ef-46e9-b0bb-56de5ebe45a7
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd
Bonchi, Filippo
3c53e89d-d280-4911-9938-eb861553d04e
Seeber, Jens
4c59db18-08ef-46e9-b0bb-56de5ebe45a7
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd

Bonchi, Filippo, Seeber, Jens and Sobocinski, Pawel (2018) Graphical conjunctive queries. In CSL 2018: 27th EACSL Annual Conference on Computer Science Logic. Leibniz International Proceedings in Informatics (LIPIcs). 23 pp .

Record type: Conference or Workshop Item (Paper)

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.

Text
GCQ - Proof
Available under License Creative Commons Attribution.
Download (1MB)

More information

Published date: 4 September 2018
Venue - Dates: Computer Science Logic 2018<br/>, Birmingham, United Kingdom, 2018-09-04 - 2018-09-07

Identifiers

Local EPrints ID: 422530
URI: http://eprints.soton.ac.uk/id/eprint/422530
PURE UUID: 7755e08d-4ee8-45c1-aef7-84ec0773af7f

Catalogue record

Date deposited: 25 Jul 2018 16:30
Last modified: 19 Jul 2019 17:06

Export record

Contributors

Author: Filippo Bonchi
Author: Jens Seeber
Author: Pawel Sobocinski

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×