Overview
Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (MATHE2, volume 43)
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About this book
Except for this preface, this study is completely self-contained. It is intended to serve both as an introduction to Quantification Theory and as an exposition of new results and techniques in "analytic" or "cut-free" methods. We use the term "analytic" to apply to any proof procedure which obeys the subformula principle (we think of such a procedure as "analysing" the formula into its successive components). Gentzen cut-free systems are perhaps the best known example of ana lytic proof procedures. Natural deduction systems, though not usually analytic, can be made so (as we demonstrated in [3]). In this study, we emphasize the tableau point of view, since we are struck by its simplicity and mathematical elegance. Chapter I is completely introductory. We begin with preliminary material on trees (necessary for the tableau method), and then treat the basic syntactic and semantic fundamentals of propositional logic. We use the term "Boolean valuation" to mean any assignment of truth values to all formulas which satisfies the usual truth-table conditions for the logical connectives. Given an assignment of truth-values to all propositional variables, the truth-values of all other formulas under this assignment is usually defined by an inductive procedure. We indicate in Chapter I how this inductive definition can be made explicit-to this end we find useful the notion of a formation tree (which we discuss earlier).
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Table of contents (17 chapters)
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Front Matter
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Propositional Logic from the Viewpoint of Analytic Tableaux
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Front Matter
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Further Topics in First-Order Logic
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Front Matter
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Authors and Affiliations
Bibliographic Information
Book Title: First-Order Logic
Authors: Raymond M. Smullyan
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge
DOI: https://doi.org/10.1007/978-3-642-86718-7
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin · Heidelberg 1968
Softcover ISBN: 978-3-642-86720-0Published: 14 April 2012
eBook ISBN: 978-3-642-86718-7Published: 06 December 2012
Edition Number: 1
Number of Pages: XII, 160