Basic Proof Theory

Introduction to proof theory and its applications in mathematical logic, theoretical computer science and artificial intelligence.

A. S. Troelstra (Author), H. Schwichtenberg (Author)

9780521779111, Cambridge University Press

Paperback, published 27 July 2000

432 pages, 3 b/w illus. 201 exercises
22.7 x 15.4 x 2.3 cm, 0.595 kg

'This is a fine book. Any computer scientist with some logical background will benefit from studying it. It is written by two of the experts in the field and comes up to their usual standards of precision and care.' Ray Turner, Computer Journal

This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.

1. Introduction
2. N-systems and H-systems
3. Gentzen systems
4. Cut elimination with applications
5. Bounds and permutations
6. Normalization for natural deduction
7. Resolution
8. Categorical logic
9. Modal and linear logic
10. Proof theory of arithmetic
11. Second-order logic
Solutions to selected exercises. Bibliography
Symbols and notation
Index.

Subject Areas: Mathematical theory of computation [UYA]