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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
First-Order Logic

First-Order Logic

Smullyan, Raymond R.

Paperback

Series: Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge, Book 43

Fiction

ISBN10: 3642867200
ISBN13: 9783642867200
Publisher: Springer Nature
Published: Apr 14 2012
Pages: 160
Weight: 0.56
Height: 0.38 Width: 6.14 Depth: 9.21
Language: English
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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