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.

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

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'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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