From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5081 Path: news.gmane.org!not-for-mail From: Lutz Schroeder , Newsgroups: gmane.science.mathematics.categories Subject: Re: making a cone universal in a faithful way Date: Tue, 04 Aug 2009 12:41:34 +0200 Message-ID: Reply-To: Lutz Schroeder , NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1249391781 23759 80.91.229.12 (4 Aug 2009 13:16:21 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 4 Aug 2009 13:16:21 +0000 (UTC) To: Dimitri Ara Original-X-From: categories@mta.ca Tue Aug 04 15:16:14 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 1MYJsD-0002K9-DY for gsmc-categories@m.gmane.org; Tue, 04 Aug 2009 15:16:13 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MYJ9c-0001JO-Gd for categories-list@mta.ca; Tue, 04 Aug 2009 09:30:08 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5081 Archived-At: Dear Dimitri, > You are right. I didn't checked very carefully the local confluence of = my > rewriting system. To get confluence, I need to add the fact that the > bimorphism f satisfies "fu =3D vf implies u =3D 1 and v =3D 1". So this= is enough > for f to be a potential isomorphism. Yes, that does the trick, and is also the best sufficient condition that I have been able to come up with in my thesis. I would guess something similar might work for the general case, but the condition is actually so strong as to be somewhat unsatisfactory. Note in particular that it fails for actual (nontrivial) isomorphisms. I poked around this problem for quite a bit back then but haven't been able to isolate a satisfactory criterion (other than the obvious one that talks explicitly about equality in a non-confluent axiom system). Good luck, Lutz --=20 -------------------------------------- PD Dr. Lutz Schr=F6der Senior Researcher DFKI Bremen=09 Safe and Secure Cognitive Systems Cartesium, Enrique-Schmidt-Str. 5 D-28359 Bremen phone: (+49) 421-218-64216 Fax: (+49) 421-218-9864216 mail: Lutz.Schroeder@dfki.de www.dfki.de/sks/staff/lschrode -------------------------------------- ------------------------------------------------------------- Deutsches Forschungszentrum f=FCr K=FCnstliche Intelligenz GmbH Firmensitz: Trippstadter Strasse 122, D-67663 Kaiserslautern Gesch=E4ftsf=FChrung: Prof. Dr. Dr. h.c. mult. Wolfgang Wahlster (Vorsitzender) Dr. Walter Olthoff Vorsitzender des Aufsichtsrats: Prof. Dr. h.c. Hans A. Aukes Amtsgericht Kaiserslautern, HRB 2313 ------------------------------------------------------------- [For admin and other information see: http://www.mta.ca/~cat-dist/ ]