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Introduction to Mathematical Logic and Type Theory : To Truth Through Proof

Introduction to Mathematical Logic and Type Theory : To Truth Through Proof - 02 edition

ISBN13: 978-1402007637

Cover of Introduction to Mathematical Logic and Type Theory : To Truth Through Proof 02 (ISBN 978-1402007637)
ISBN13: 978-1402007637
ISBN10: 1402007639
Cover type:
Edition/Copyright: 02
Publisher: Kluwer Academic Publishers
Published: 2002
International: No

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Introduction to Mathematical Logic and Type Theory : To Truth Through Proof - 02 edition

ISBN13: 978-1402007637

Peter B. Andrews

ISBN13: 978-1402007637
ISBN10: 1402007639
Cover type:
Edition/Copyright: 02
Publisher: Kluwer Academic Publishers

Published: 2002
International: No
Summary

This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability.

The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory.

Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises.

Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.

Table of Contents

1. Propositional Calculus.
2. First-Order Logic.
3. Provability and Refutability.
4. Further Topics in First-Order Logic.
5. Type Theory.
6. Formalized Number Theory.
7. Incompleteness and Undecidability

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