From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4677 Path: news.gmane.org!not-for-mail From: zackluo@j4.com Newsgroups: gmane.science.mathematics.categories Subject: preprint available Date: Sun, 02 Nov 2008 23:54:24 -0600 (CST) Message-ID: Reply-To: zackluo@j4.com NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241020100 14342 80.91.229.2 (29 Apr 2009 15:48:20 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:48:20 +0000 (UTC) To: categories Original-X-From: rrosebru@mta.ca Mon Nov 3 09:59:27 2008 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 03 Nov 2008 09:59:27 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Kwzq2-0003Q9-VV for categories-list@mta.ca; Mon, 03 Nov 2008 09:51:27 -0400 Original-Sender: categories@mta.ca Precedence: bulk X-Keywords: X-UID: 2 Original-Lines: 10 Xref: news.gmane.org gmane.science.mathematics.categories:4677 Archived-At: Clone Theory: Its Syntax and Semantics, Applications to Universal Algebra, Lambda Calculus and Algebraic Logic Author: Zhaohua Luo Abstract: The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this purpose are various clones over a full subcategory of a category. We show that the syntax of equational logic, lambda calculus and first order logic can be represented as clones or right algebras of clones over the set of positive integers. The semantics is then represented by structures derived from left algebras of these clones. URL: http://www.algebraic.net/cag/ct.pdf