Introduction to Proof Theory
by Gilles Dowek
Publisher: ESSLLI 2001
Number of pages: 82
These are the course notes for the 13th European Summer School in Logic, Language and Information. Contents: Predicate Logic; Extension of Predicate Logic; Type Theory; Cut Elimination in Predicate Logic; Cut Elimination in Predicate Logic Modulo.
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by Jon Barwise, John Etchemendy - Center for the Study of Language
The book covers the boolean connectives, formal proof techniques, quantifiers, basic set theory, induction, proofs of soundness and completeness for propositional and predicate logic, and an accessible sketch of Godel's first incompleteness theorem.
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These lecture notes give a brief introduction to logic, with including the resolution method of theorem-proving and its relation to the programming language Prolog. Formal logic is used for specifying and verifying computer systems.
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This textbook is intended to communicate something about proof, sets, and logic. It is about the foundations of mathematics, a subject which results when mathematicians examine the subject matter and the practice of their own subject very carefully.
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This book is a self-contained introduction to interactive proof in higher-order logic, using the proof assistant Isabelle. It is a tutorial for potential users. The book has three parts: Elementary Techniques; Logic and Sets; Advanced Material.