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Basic Proof Theory

Basic Proof Theory

2nd Edition

$59.99 (P)

Part of Cambridge Tracts in Theoretical Computer Science

  • Date Published: July 2000
  • availability: Available
  • format: Paperback
  • isbn: 9780521779111

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  • This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of first-order logic formalization. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic, logic programming theory, category theory, modal logic, linear logic, first-order arithmetic and second-order logic. In each case the authors illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. For the new edition, they have rewritten many sections to improve clarity, added new sections on cut elimination, and included solutions to selected exercises. 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.

    • Fills the gap between basic textbooks on logic and advanced monographs on proof theory
    • Brings together basic results which are spread over many papers and books in the literature
    • Written by two of the world's leading authorities
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    Reviews & endorsements

    '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

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    Product details

    • Edition: 2nd Edition
    • Date Published: July 2000
    • format: Paperback
    • isbn: 9780521779111
    • length: 432 pages
    • dimensions: 227 x 154 x 23 mm
    • weight: 0.595kg
    • contains: 3 b/w illus. 201 exercises
    • availability: Available
  • Table of Contents

    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.

  • Authors

    A. S. Troelstra, Universiteit van Amsterdam

    H. Schwichtenberg, Universität Munchen

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