A Short Introduction to Intuitionistic Logic

Grigori Mints (Autor)

Buch | Softcover

131 Seiten

2013
Springer-Verlag New York Inc.
978-1-4757-7319-4 (ISBN)

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Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs. to make the material more accessible, basic techniques are presented first for propositional logic; Part II contains extensions to predicate logic. This material provides an introduction and a safe background for reading research literature in logic and computer science as well as advanced monographs. Readers are assumed to be familiar with basic notions of first order logic. One device for making this book short was inventing new proofs of several theorems. The presentation is based on natural deduction. The topics include programming interpretation of intuitionistic logic by simply typed lambda-calculus (Curry-Howard isomorphism), negative translation of classical into intuitionistic logic, normalization of natural deductions, applications to category theory, Kripke models, algebraic and topological semantics, proof-search methods, interpolation theorem. The text developed from materal for several courses taught at Stanford University in 1992-1999.

Intuitionistic Predicate Logic.- Natural Deduction System NJ.- Kripke Models for Predicate Logic.- Systems LJm, LJ.- Proof-Search in Predicate Logic.- Preliminaries.- Natural Deduction for Propositional Logic.- Negative Translation: Glivenko’s Theorem.- Program Interpretation of Intuitionistic Logic.- Computations with Deductions.- Coherence Theorem.- Kripke Models.- Gentzen-type Propositional System LJpm.- Topological Completeness.- Proof-search.- System LJp.- Interpolation Theorem.

Reihe/Serie	University Series in Mathematics
Zusatzinfo	IX, 131 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Geisteswissenschaften ► Philosophie ► Logik
	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	1-4757-7319-6 / 1475773196
ISBN-13	978-1-4757-7319-4 / 9781475773194
Zustand	Neuware