From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4970 Path: news.gmane.org!not-for-mail From: Steve Vickers Newsgroups: gmane.science.mathematics.categories Subject: Re: database theory based on Heyting algebra instead of Boolean algebra Date: Thu, 11 Jun 2009 14:03:11 +0100 Message-ID: Reply-To: Steve Vickers NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1244728522 24420 80.91.229.12 (11 Jun 2009 13:55:22 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 11 Jun 2009 13:55:22 +0000 (UTC) To: "Vasili I. Galchin" , Original-X-From: categories@mta.ca Thu Jun 11 15:55:20 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1MEkkR-0004Qe-LM for gsmc-categories@m.gmane.org; Thu, 11 Jun 2009 15:55:19 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MEk6Y-0000ND-6n for categories-list@mta.ca; Thu, 11 Jun 2009 10:14:06 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4970 Archived-At: Dear Vasili, I'm not sure how much this will answer your questions, but there was some research towards the end of the last century relating databases and powerdomains. In a sense, then, the associated logic of database queries is that of the open sets of the domain, i.e. geometric logic, and hence (at least in its finitary form) a fragment of intuitionistic logic. The names I associate with this work are Carl Gunter and Peter Buneman. I wrote a 1992 paper "Geometric Theories and Databases" that was inspired by them, though its main content was a topos-theoretic construction. Regards, Steve Vickers. Vasili I. Galchin wrote: > Hello, > > I'm sorry that this a bit off topic (but both algebras are > categories), but I don't know where to post in order to get an intelligent > answer. Is there any research to base data base queries on Heyting algebra, > i.e. intuistionistic logic? > > Thanks, > > Vasili > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ] [For admin and other information see: http://www.mta.ca/~cat-dist/ ]