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.
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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
"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
Explores topics that are at the cutting edge of developments
in computer science, while preserving the integrity of traditional
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.
Provides over 500 exercises.
- Uses familiar examples to ease students into new
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
6. A Proof System for First-Order Logic and Gödel's
Appendix A. A Simple Timetable of Mathematical Logic and
Appendix B. Dedekind-Peano Number System.
Appendix C. Writing Up an Inductive Definition or Proof.
Appendix D. FL Propositional Logic.