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 J. Girard, Y. Lafont, P. Taylor - Cambridge University Press
This little book comes from a short graduate course on typed lambda-calculus given at the Universite Paris. It is not intended to be encyclopedic and the selection of topics was really quite haphazard. Some very basic knowledge of logic is needed.
by T. Nipkow, L.C. Paulson, M. Wenzel - Springer
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.
by Lawrence C Paulson - University of Cambridge
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.
by Greg Restall - consequently.org
A textbook in philosophical logic, accessible to someone who's done only an intro course in logic, covering some model theory and proof theory of propositional logic, and predicate logic. User-friendly and philosophically motivated presentation.