First-Order Logic

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Springer Berlin Heidelberg, 1 gen 1971 - 160 pagine
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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Informazioni sull'autore (1971)

Raymond Merrill Smullyan was born in Far Rockaway, Queens, New York on May 25, 1919. He received a bachelor's degree in mathematics from the University of Chicago and a Ph.D. from Princeton University. He taught at Princeton, Yeshiva University, Lehman College of the City University of New York, and Indiana University. He also performed magic under the stage name Five-Ace Merrill at nightclubs like the Pump Room in Chicago. He was a puzzle-creating logician who wrote many books including The Chess Mysteries of the Arabian Knights, The Lady or the Tiger?: And Other Logic Puzzles, Alice in Puzzle-Land: A Carrollian Tale for Children, and The Magic Garden of George B and Other Logic Puzzles. He died on February 6, 2017 at the age of 97.

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