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First-Order Logic

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 189/5 ( reviews)

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Book Synopsis First-Order Logic by : Raymond R. Smullyan

Download or read book First-Order Logic written by Raymond R. Smullyan. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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).

First-Order Logic and Automated Theorem Proving

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 575/5 ( reviews)

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Book Synopsis First-Order Logic and Automated Theorem Proving by : Melvin Fitting

Download or read book First-Order Logic and Automated Theorem Proving written by Melvin Fitting. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: There are many kinds of books on formal logic. Some have philosophers as their intended audience, some mathematicians, some computer scientists. Although there is a common core to all such books they will be very dif ferent in emphasis, methods, and even appearance. This book is intended for computer scientists. But even this is not precise. Within computer sci ence formal logic turns up in a number of areas, from program verification to logic programming to artificial intelligence. This book is intended for computer scientists interested in automated theorem proving in classical logic. To be more precise yet, it is essentially a theoretical treatment, not a how-to book, although how-to issues are not neglected. This does not mean, of course, that the book will be of no interest to philosophers or mathematicians. It does contain a thorough presentation of formal logic and many proof techniques, and as such it contains all the material one would expect to find in a course in formal logic covering completeness but not incompleteness issues. The first item to be addressed is, what are we talking about and why are we interested in it. We are primarily talking about truth as used in mathematical discourse, and our interest in it is, or should be, self-evident. Truth is a semantic concept, so we begin with models and their properties. These are used to define our subject.

First-order Logic

1998 Mathematics
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Release : 1998
Genre : Mathematics
Kind : eBook
Book Rating : 666/5 ( reviews)

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Book Synopsis First-order Logic by : Leigh S. Cauman

Download or read book First-order Logic written by Leigh S. Cauman. This book was released on 1998. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to principles and notation of modern symbolic logic, for those with no prior courses. The structure of material follows that of Quine's Methods of Logic, and may be used as an introduction to that work, with sections on truth-functional logic, predicate logic, relational logic, and identity and description. Exercises are based on problems designed by authors including Quine, John Cooley, Richard Jeffrey, and Lewis Carroll. Annotation copyrighted by Book News, Inc., Portland, OR

A Concise Introduction to Logic

2017-02-06
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Release : 2017-02-06
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Kind : eBook
Book Rating : 437/5 ( reviews)

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Book Synopsis A Concise Introduction to Logic by : Craig DeLancey

Download or read book A Concise Introduction to Logic written by Craig DeLancey. This book was released on 2017-02-06. Available in PDF, EPUB and Kindle. Book excerpt:

Extensions of First-Order Logic

1996-03-29 Computers
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Release : 1996-03-29
Genre : Computers
Kind : eBook
Book Rating : 356/5 ( reviews)

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Book Synopsis Extensions of First-Order Logic by : Maria Manzano

Download or read book Extensions of First-Order Logic written by Maria Manzano. This book was released on 1996-03-29. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to many-sorted logic as an extension of first-order logic.

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