From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4878 Path: news.gmane.org!not-for-mail From: Zinovy Diskin Newsgroups: gmane.science.mathematics.categories Subject: Re: sketch theory Date: Sun, 24 May 2009 20:18:08 -0400 Message-ID: Reply-To: Zinovy Diskin NNTP-Posting-Host: lo.gmane.org Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1243265446 9214 80.91.229.12 (25 May 2009 15:30:46 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 25 May 2009 15:30:46 +0000 (UTC) To: Andre.Rodin@ens.fr, Original-X-From: categories@mta.ca Mon May 25 17:30:39 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 1M8c8M-0006Fp-P4 for gsmc-categories@m.gmane.org; Mon, 25 May 2009 17:30:38 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1M8bcS-0005Gu-V5 for categories-list@mta.ca; Mon, 25 May 2009 11:57:41 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4878 Archived-At: Let me make a few clarifying remarks On Fri, May 22, 2009 at 8:44 PM, wrote: > I came across this recent paper by Diskin&Wolter > > http://www.cs.toronto.edu/~zdiskin/Pubs/ACCAT-07.pdf > > where the authors propose a version of sketch-based syntax for Computer S= cience > purposes. The main idea here (as far as I understood the paper) is to use > sketches as arities of predicates. I heard about similar ideas from Rene > Guitart in private conversations (but Rene's approach is algebraic rather= than > logical). our version of sketches is intended for use in software engineering, not only in computer science. The difference between them is like the difference between, say, electrical engineering and physics. Predicate arities may be objects of any a priori chosen good category, e.g., sketches built in a previous step, but this is not the main idea. Relation of Makkai's generalized sketches to classical sketches is, roughly, like relation of a general first-order theory a la Tarski to a particular family of theories like, e.g., lattice theory. The former provide a general framework, in which the user can define any theory she likes. The latter is a family of particular instantiations of the framework. The fact that this family is expressive enough to specify any structure is another story. A first-order signature contains operation and predicate symbols. Similarly, a generalized sketch signature may contain operation symbols too (whose arities are In-Out spans). Definitions and some details can be found in Report referenced as [6] in the paper above. ZD Looking at GBLS briefly I couldn't immediately grasp if your and > Atish Bagchi's approach to graph-based logic is based on similar ideas or= your > approach is quite different. I certainly should read GBLS more carefully = for > discussing it but I would grateful for a hint. > > Andrei > > > > Selon Charles Wells : > >> I have not kept up with the field very well, but I can recommend these >> works: >> >> Peter Johnstone, *Sketches of an Elephant*, Vol. 2, OUP 2003: the chapte= r on >> sketches. =C2=A0(I am in rural Wisconsin at the moment asnd don't have a= ccess to >> the book. =C2=A0If OUP would make its pages available to look at on Amaz= on I >> could have told you the exact page.) >> >> Bagchi and Wells, *Graph Based Logic and Sketches*, here: >> >> http://arxiv.org/PS_cache/arxiv/pdf/0809/0809.3023v1.pdf >> >> Also Kinoshita, et al 1997, referred to in GBLS. =C2=A0There might be re= levant >> papers since 1993 mentioned in the Elephant, too. >> >> Category people: =C2=A0If you can suggest other papers that should be in= cluded, >> let me know soon, and I will revise the sketches paper to include them (= and >> the ones I mentioned above). >> >> Charles Wells >> >> > >