
Logic for Mathematics and Computer Science, 1/e
Stanley N. Burris, University of Waterloo
Published August, 1997 by Prentice Hall Engineering/Science/Mathematics
Copyright 1998, 420 pp.
Cloth
ISBN 0132859742

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Unlike other texts on mathematical logic that are either too advanced,
too sparse in examples or exercises, too traditional in coverage,
or too philosophical in approach, this text provides an elementary
"handson" presentation of important mathematical logic topics, new
and old, that is readily accessible and relevant to all students of
the mathematical sciences  not just those in traditional pure mathematics.
Assumes no background in abstract algebra or analysis
 yet focuses clearly on mathematical logic: logic for
mathematics and computer science that is developed and analyzed using
mathematical methods.
Explores topics that are at the cutting edge of developments
in computer science, while preserving the integrity of traditional
logic.
Stresses that there are several selfcontained proof
systems of interest to mathematical logic  some more suitable
than others for particular kinds of questions.
Presents elementary traditional logic sidebyside with
its algorithmic aspects  i.e., the syntax and semantics of firstorder
logic up to completeness and compactness, and developments in theorem
proving that were inspired by the possibilities of using computers
(e.g., Robinson's resolution theorem proving and the KnuthBendix
procedure to obtain term rewrite systems.)
Provides detailed explanations and examples throughout.
Includes historical detail to tie concepts together.
Features over 200 examples worked out in detail.
 Uses familiar examples to ease students into new
material.
Provides over 500 exercises.
Contains two substantial worksheets on Peano's
Axioms and the FL propositional logic.
Offers supplementary materials on the internet 
where students can experience automated logical algorithms in action.
I. QUANTIFIERFREE LOGICS.
1. From Aristotle to Boole.
2. Propositional Logic.
3. Equational Logic.
4. Predicate Clause Logic.
II. LOGIC WITH QUANTIFIERS.
5. FirstOrder Logic: Introduction, and Fundamental Results
on Semantics.
6. A Proof System for FirstOrder Logic and Gödel's
Completeness Theorem.
Appendix A. A Simple Timetable of Mathematical Logic and
Computing.
Appendix B. DedekindPeano Number System.
Appendix C. Writing Up an Inductive Definition or Proof.
Appendix D. FL Propositional Logic.
Bibliography.
Index.
