First-Order Logic by Raymond M Smullyan

First-Order Logic by Raymond M Smullyan

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).

Raymond Smullyan received his PhD from Princeton University and taught at Dartmouth, Princeton, Indiana University, and New York's Lehman College. Best known for his mathematical and creative logic puzzles and games, he was also a concert pianist and a magician. He wrote over a dozen books of logic puzzles and texts on mathematical logic. Raymond Smullyan: The Merry Prankster
Raymond Smullyan (1919-2017), mathematician, logician, magician, creator of extraordinary puzzles, philosopher, pianist, and man of many parts. The first Dover book by Raymond Smullyan was First-Order Logic (1995). Recent years have brought a number of his magical books of logic and math puzzles: The Lady or the Tiger (2009); Satan, Cantor and Infinity (2009); an original, never-before-published collection, King Arthur in Search of His Dog and Other Curious Puzzles (2010); and Set Theory and the Continuum Problem (with Melvin Fitting, also reprinted by Dover in 2010). More will be coming in subsequent years.

In the Author's Own Words:
Recently, someone asked me if I believed in astrology. He seemed somewhat puzzled when I explained that the reason I don't is that I'm a Gemini.

Some people are always critical of vague statements. I tend rather to be critical of precise statements: they are the only ones which can correctly be labeled 'wrong.' -- Raymond Smullyan

Critical Acclaim for The Lady or the Tiger:
Another scintillating collection of brilliant problems and paradoxes by the most entertaining logician and set theorist who ever lived. -- Martin Gardner

SKU	Unavailable
ISBN 13	9780486683706
ISBN 10	0486683702
Title	First-Order Logic
Author	Raymond M Smullyan
Condition	Unavailable
Binding Type	Paperback
Publisher	Dover Publications Inc.
Year published	2000-02-01
Number of pages	176
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note	Unavailable