From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4540 Path: news.gmane.org!not-for-mail From: Luigi Santocanale Newsgroups: gmane.science.mathematics.categories Subject: Re: logics for model checking Date: Wed, 03 Sep 2008 22:59:53 +0200 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=windows-1252; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241020014 13769 80.91.229.2 (29 Apr 2009 15:46:54 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:46:54 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Sep 3 18:59:51 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 03 Sep 2008 18:59:51 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Kb0L3-0006Kp-5i for categories-list@mta.ca; Wed, 03 Sep 2008 18:56:33 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 7 Original-Lines: 39 Xref: news.gmane.org gmane.science.mathematics.categories:4540 Archived-At: Hi, > Any other thoughts, suggestions, or references would be > appreciated. In L. S. Completions of \mu-algebras. APAL, 154(1):27-50, May 2008. I studied the problem of the completeness of the modal mu-calculus from=20 an finitary algebraic point of view. In that paper some categorical=20 ideas, mainly from W. Tholen, Pro-categories and multiadjoint functors, Canad. J. Math. 36=20 (1) (1984) 144=96155. play the relevant role. The challenge is to prove that in free modal=20 \mu-algebras, the relation \mu.f =3D \bigvee_{n>=3D0} f^n(\bot) holds -- where \mu.f, the least fixpoint of f, is axiomatized by=20 equational implications and free modal \mu-algebras are not known to be=20 complete. Best, Luigi --=20 Luigi Santocanale LIF/CMI Marseille T=E9l: 04 91 11 35 74 http://www.cmi.univ-mrs.fr/~lsantoca/ Fax: 04 91 11 36 02 =09