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Cambridge Tracts in Theoretical Computer Science #43: Basic Proof Theory

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Synopses & Reviews

Publisher Comments:

'This excellent introduction to the basic ideas of structural proof theory--the theory of formal proofs as combinatorial structures--uses cut elimination and normalization as central tools. The authors thoroughly discuss and compare various types of formalization of first-order logic, in particular Hilbert systems, Gentzen systems, and Natural Deduction. They give examples of several application areas 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 Troelstra and Schwichtenberg illustrate the methods in relatively simple situations and then apply them elsewhere in more complex settings. The chapters feature numerous exercises for student practice. With the only prerequisite a standard course in first-order logic, the book is ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science, and artificial intelligence.'

Synopsis:

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. 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. 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.

Synopsis:

This is an introduction to the basic ideas of structural proof theory. 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.

Synopsis:

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.

Synopsis:

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

Description:

Includes bibliographical references (p. 379-403) and index.

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.

Product Details

ISBN:
9780521779111
Other:
Troelstra, Anne S.
Author:
Schwichtenberg, H.
Author:
Van Rijsbergen, C. J.
Author:
Troelstra, Anne S.
Author:
C. J. van Rijsbergen
Author:
Troelstra, A. S.
Publisher:
Cambridge University Press
Location:
Cambridge
Subject:
General
Subject:
Logic
Subject:
Logic Design
Subject:
Computer Mathematics
Subject:
Programming - Software Development
Subject:
Proof theory
Subject:
General Computers
Subject:
Proof theory Proof theory
Subject:
Artificial Intelligence - Fuzzy Logic
Subject:
Programming Languages - General
Edition Number:
2
Edition Description:
Trade paper
Series:
Cambridge Tracts in Theoretical Computer Science
Series Volume:
105-5843
Publication Date:
20020131
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
3 b/w illus. 201 exercises
Pages:
432
Dimensions:
8.98x6.26x1.03 in. 1.39 lbs.

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Cambridge Tracts in Theoretical Computer Science #43: Basic Proof Theory New Trade Paper
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Product details 432 pages Cambridge University Press - English 9780521779111 Reviews:
"Synopsis" by , 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. 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. 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.
"Synopsis" by , This is an introduction to the basic ideas of structural proof theory. 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.
"Synopsis" by , 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.
"Synopsis" by , Introduction to proof theory and its applications in mathematical logic, theoretical computer science and artificial intelligence.
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