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Cambridge Tracts in Theoretical Computer Science #43: Basic Proof Theoryby Anne S. Troelstra
Synopses & ReviewsPublisher Comments:'This excellent introduction to the basic ideas of structural proof theorythe theory of formal proofs as combinatorial structuresuses cut elimination and normalization as central tools. The authors thoroughly discuss and compare various types of formalization of firstorder logic, in particular Hilbert systems, Gentzen systems, and Natural Deduction. They give examples of several application areas namely, the metamathematics of pure firstorder logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; firstorder arithmetic; and secondorder 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 firstorder 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 firstorder 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 firstorder 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 firstorder logic formalization. Examples are given of several areas of application, namely: the metamathematics of pure firstorder logic, logic programming theory, category theory, modal logic, linear logic, firstorder arithmetic and secondorder 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 firstorder 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. 379403) and index.
Table of Contents1. Introduction; 2. Nsystems and Hsystems; 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. Secondorder logic; Solutions to selected exercises. Bibliography; Symbols and notation; Index.
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