## Logic for Mathematics and Computer Science, 1/e

Stanley N. Burris, University of Waterloo

Published August, 1997 by Prentice Hall Engineering/Science/Mathematics

Cloth
ISBN 0-13-285974-2

mailings
on this subject.

Logic-Mathematics

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 "hands-on" 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 self-contained proof systems of interest to mathematical logic -- some more suitable than others for particular kinds of questions.
Presents elementary traditional logic side-by-side with its algorithmic aspects -- i.e., the syntax and semantics of first-order 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 Knuth-Bendix 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. QUANTIFIER-FREE LOGICS.
1. From Aristotle to Boole.
2. Propositional Logic.
3. Equational Logic.
4. Predicate Clause Logic.

II. LOGIC WITH QUANTIFIERS.
5. First-Order Logic: Introduction, and Fundamental Results on Semantics.
6. A Proof System for First-Order Logic and Gödel's Completeness Theorem.
Appendix A. A Simple Timetable of Mathematical Logic and Computing.
Appendix B. Dedekind-Peano Number System.
Appendix C. Writing Up an Inductive Definition or Proof.
Appendix D. FL Propositional Logic.
Bibliography.
Index.