文档介绍：A General Algebraic Semantics
for Sentential Logics
LECTURE NOTES IN LOGIC
A Publication of
THE ASSOCIATION FOR SYMBOLIC LOGIC
Editorial Board:
Anand Pillay, Managing Editor
Jeremy Avigad
Vladimir Kanovei
Shaughan Lavine
Steffen Lempp
Thomas Wilke
LECTURE NOTES IN LOGIC 7
A General Algebraic Semantics
for Sentential Logics
Second Edition
Josep Maria Font
Department of Probability, Logic and Statistics
University of Barcelona
Ramon Jansana
Department of Logic, History and Philosophy of Science
University of Barcelona
ASSOCIATION FOR SYMBOLIC LOGIC
Association for Symbolic Logic
Richard A. Shore, Publisher
Department of Mathematics
Cornell University
Malott Hall
Ithaca NY 14853 USA
Copyright
c 2009 by the Association for Symbolic Logic.
All rights reserved. No part of the material protected by this copyright notice may
be reproduced or utilized in any form, electronic or mechanical, including photo-
copying, recording, or by any information storage and retrieval system, without
written permission from the Association for Symbolic Logic.
Publisher’s note: This book was typeset in LATEX by the authors, using the ASL
documentclass . The fonts are Monotype Times New Roman.
14 13 12 11 10 09 08 07 06 05 5 4 3 2 1
CONTENTS
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
CHAPTER 1. GENERALITIES ON ABSTRACT LOGICS
AND SENTENTIAL LOGICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
CHAPTER 2. ABSTRACT LOGICS AS MODELS
OF SENTENTIAL LOGICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
. Models and full models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
. S-algebras. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
. The lattice of full models over an algebra . . . . . . . . . . . . . . . . . . . . . 40
2