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This completely selfcontained study, widely considered the best book in the field, is intended to serve both as an introduction to quantification theory and as an exposition of new results and techniques in "analytic" or "cutfree" methods. Impressed by the simplicity and mathematical elegance of the tableau point of view, the author focuses on it here.After preliminary material on tress (necessary for the tableau method), Part I deals with propositional logic from the viewpoint of analytic tableaux, covering such topics as formulas or propositional logic, Boolean valuations and truth sets, the method of tableaux and compactness.Part II covers firstorder logic, offering detailed treatment of such matters as firstorder analytic tableaux, analytic consistency, quantification theory, magic sets, and analytic versus synthetic consistency properties.Part III continues coverage of firstorder logic. Among the topics discussed are Gentzen systems, elimination theorems, prenex tableaux, symmetric completeness theorems, and system linear reasoning.Raymond M. Smullyan is a wellknown logician and inventor of mathematical and logical puzzles. In this book he has written a stimulating and challenging exposition of firstorder logic that will be welcomed by logicians, mathematicians, and anyone interested in the field.
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