First Order Logic

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First-Order Logic

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Author : Raymond R. Smullyan
Publisher : Springer Science & Business Media
ISBN 13 : 3642867189
Total Pages : 167 pages
Book Rating : 4.6/5 (428 download)

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

Download or read book First-Order Logic written by Raymond R. Smullyan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 167 pages. 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

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Author : Melvin Fitting
Publisher : Springer Science & Business Media
ISBN 13 : 1468403575
Total Pages : 258 pages
Book Rating : 4.4/5 (684 download)

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 and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 258 pages. 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.

A Concise Introduction to Logic

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Author : Craig DeLancey
Publisher : Open SUNY Textbooks
ISBN 13 : 9781942341437
Total Pages : pages
Book Rating : 4.3/5 (414 download)

Book Synopsis A Concise Introduction to Logic by : Craig DeLancey

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

Extensions of First-Order Logic

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Author : Maria Manzano
Publisher : Cambridge University Press
ISBN 13 : 9780521354356
Total Pages : 414 pages
Book Rating : 4.3/5 (543 download)

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

Download or read book Extensions of First-Order Logic written by Maria Manzano and published by Cambridge University Press. This book was released on 1996-03-29 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to many-sorted logic as an extension of first-order logic.

First-Order Logic

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Author : John Heil
Publisher : Hackett Publishing
ISBN 13 : 1647920108
Total Pages : 303 pages
Book Rating : 4.6/5 (479 download)

Book Synopsis First-Order Logic by : John Heil

Download or read book First-Order Logic written by John Heil and published by Hackett Publishing. This book was released on 2021-10-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In his introduction to this most welcome republication (and second edition) of his logic text, Heil clarifies his aim in writing and revising this book: 'I believe that anyone unfamiliar with the subject who set out to learn formal logic could do so relying solely on [this] book. That, in any case, is what I set out to create in writing An Introduction to First-Order Logic.' Heil has certainly accomplished this with perhaps the most explanatorily thorough and pedagogically rich text I’ve personally come across. "Heil's text stands out as being remarkably careful in its presentation and illuminating in its explanations—especially given its relatively short length when compared to the average logic textbook. It hits all of the necessary material that must be covered in an introductory deductive logic course, and then some. It also takes occasional excursions into side topics, successfully whetting the reader’s appetite for more advanced studies in logic. "The book is clearly written by an expert who has put in the effort for his readers, bothering at every step to see the point and then explain it clearly to his readers. Heil has found some very clever, original ways to introduce, motivate, and otherwise teach this material. The author's own special expertise and perspective—especially when it comes to tying philosophy of mind, linguistics, and philosophy of language into the lessons of logic—make for a creative and fresh take on basic logic. With its unique presentation and illuminating explanations, this book comes about as close as a text can come to imitating the learning environment of an actual classroom. Indeed, working through its presentations carefully, the reader feels as though he or she has just attended an illuminating lecture on the relevant topics!" —Jonah Schupbach, University of Utah

The Language of First-Order Logic, Including the Macintosh Program Tarski's World 4.0

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Author : Jon Barwise
Publisher : Center for the Study of Language and Information Publications
ISBN 13 : 9780937073995
Total Pages : 336 pages
Book Rating : 4.0/5 (739 download)

Book Synopsis The Language of First-Order Logic, Including the Macintosh Program Tarski's World 4.0 by : Jon Barwise

Download or read book The Language of First-Order Logic, Including the Macintosh Program Tarski's World 4.0 written by Jon Barwise and published by Center for the Study of Language and Information Publications. This book was released on 1993-08-01 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Language of First-Order Logic is a complete introduction to first-order symbolic logic, consisting of a computer program and a text. The program, an aid to learning and using symbolic notation, allows one to construct symbolic sentences and possible worlds, and verify that a sentence is well formed. The truth or falsity of a sentence can be determined by playing a deductive game with the computer.

First-order Logic

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Author : Leigh S. Cauman
Publisher : Walter de Gruyter
ISBN 13 : 9783110157666
Total Pages : 356 pages
Book Rating : 4.1/5 (576 download)

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

Download or read book First-order Logic written by Leigh S. Cauman and published by Walter de Gruyter. This book was released on 1998 with total page 356 pages. 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

Metalogic

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Author : Geoffrey Hunter
Publisher : Univ of California Press
ISBN 13 : 9780520023567
Total Pages : 306 pages
Book Rating : 4.0/5 (235 download)

Book Synopsis Metalogic by : Geoffrey Hunter

Download or read book Metalogic written by Geoffrey Hunter and published by Univ of California Press. This book was released on 1973-06-26 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work makes available to readers without specialized training in mathematics complete proofs of the fundamental metatheorems of standard (i.e., basically truth-functional) first order logic. Included is a complete proof, accessible to non-mathematicians, of the undecidability of first order logic, the most important fact about logic to emerge from the work of the last half-century. Hunter explains concepts of mathematics and set theory along the way for the benefit of non-mathematicians. He also provides ample exercises with comprehensive answers.

First-Order Modal Logic

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Author : M. Fitting
Publisher : Springer Science & Business Media
ISBN 13 : 9401152926
Total Pages : 300 pages
Book Rating : 4.4/5 (11 download)

Book Synopsis First-Order Modal Logic by : M. Fitting

Download or read book First-Order Modal Logic written by M. Fitting and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.

Modelling Puzzles in First Order Logic

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Author : Adrian Groza
Publisher : Springer Nature
ISBN 13 : 3030625478
Total Pages : 344 pages
Book Rating : 4.0/5 (36 download)

Book Synopsis Modelling Puzzles in First Order Logic by : Adrian Groza

Download or read book Modelling Puzzles in First Order Logic written by Adrian Groza and published by Springer Nature. This book was released on 2021-10-26 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keeping students involved and actively learning is challenging. Instructors in computer science are aware of the cognitive value of modelling puzzles and often use logical puzzles as an efficient pedagogical instrument to engage students and develop problem-solving skills. This unique book is a comprehensive resource that offers teachers and students fun activities to teach and learn logic. It provides new, complete, and running formalisation in Propositional and First Order Logic for over 130 logical puzzles, including Sudoku-like puzzles, zebra-like puzzles, island of truth, lady and tigers, grid puzzles, strange numbers, or self-reference puzzles. Solving puzzles with theorem provers can be an effective cognitive incentive to motivate students to learn logic. They will find a ready-to-use format which illustrates how to model each puzzle, provides running implementations, and explains each solution. This concise and easy-to-follow textbook is a much-needed support tool for students willing to explore beyond the introductory level of learning logic and lecturers looking for examples to heighten student engagement in their computer science courses.

First Order Categorical Logic

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Author : M. Makkai
Publisher : Springer
ISBN 13 : 3540371001
Total Pages : 317 pages
Book Rating : 4.5/5 (43 download)

Book Synopsis First Order Categorical Logic by : M. Makkai

Download or read book First Order Categorical Logic written by M. Makkai and published by Springer. This book was released on 2006-11-15 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Classical First-Order Logic

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Author : Stewart Shapiro
Publisher : Cambridge University Press
ISBN 13 : 1108991521
Total Pages : 89 pages
Book Rating : 4.1/5 (89 download)

Book Synopsis Classical First-Order Logic by : Stewart Shapiro

Download or read book Classical First-Order Logic written by Stewart Shapiro and published by Cambridge University Press. This book was released on 2022-05-19 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: One is often said to be reasoning well when they are reasoning logically. Many attempts to say what logical reasoning is have been proposed, but one commonly proposed system is first-order classical logic. This Element will examine the basics of first-order classical logic and discuss some surrounding philosophical issues. The first half of the Element develops a language for the system, as well as a proof theory and model theory. The authors provide theorems about the system they developed, such as unique readability and the Lindenbaum lemma. They also discuss the meta-theory for the system, and provide several results there, including proving soundness and completeness theorems. The second half of the Element compares first-order classical logic to other systems: classical higher order logic, intuitionistic logic, and several paraconsistent logics which reject the law of ex falso quodlibet.

First Order Mathematical Logic

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Author : Angelo Margaris
Publisher : Courier Corporation
ISBN 13 : 9780486662695
Total Pages : 244 pages
Book Rating : 4.6/5 (626 download)

Book Synopsis First Order Mathematical Logic by : Angelo Margaris

Download or read book First Order Mathematical Logic written by Angelo Margaris and published by Courier Corporation. This book was released on 1990-01-01 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Attractive and well-written introduction." — Journal of Symbolic Logic The logic that mathematicians use to prove their theorems is itself a part of mathematics, in the same way that algebra, analysis, and geometry are parts of mathematics. This attractive and well-written introduction to mathematical logic is aimed primarily at undergraduates with some background in college-level mathematics; however, little or no acquaintance with abstract mathematics is needed. Divided into three chapters, the book begins with a brief encounter of naïve set theory and logic for the beginner, and proceeds to set forth in elementary and intuitive form the themes developed formally and in detail later. In Chapter Two, the predicate calculus is developed as a formal axiomatic theory. The statement calculus, presented as a part of the predicate calculus, is treated in detail from the axiom schemes through the deduction theorem to the completeness theorem. Then the full predicate calculus is taken up again, and a smooth-running technique for proving theorem schemes is developed and exploited. Chapter Three is devoted to first-order theories, i.e., mathematical theories for which the predicate calculus serves as a base. Axioms and short developments are given for number theory and a few algebraic theories. Then the metamathematical notions of consistency, completeness, independence, categoricity, and decidability are discussed, The predicate calculus is proved to be complete. The book concludes with an outline of Godel's incompleteness theorem. Ideal for a one-semester course, this concise text offers more detail and mathematically relevant examples than those available in elementary books on logic. Carefully chosen exercises, with selected answers, help students test their grasp of the material. For any student of mathematics, logic, or the interrelationship of the two, this book represents a thought-provoking introduction to the logical underpinnings of mathematical theory. "An excellent text." — Mathematical Reviews

Duality and Definability in First Order Logic

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Author : Michael Makkai
Publisher : American Mathematical Soc.
ISBN 13 : 0821825658
Total Pages : 106 pages
Book Rating : 4.8/5 (218 download)

Book Synopsis Duality and Definability in First Order Logic by : Michael Makkai

Download or read book Duality and Definability in First Order Logic written by Michael Makkai and published by American Mathematical Soc.. This book was released on 1993 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using the theory of categories as a framework, this book develops a duality theory for theories in first order logic in which the dual of a theory is the category of its models with suitable additional structure. This duality theory resembles and generalizes M. H. Stone's famous duality theory for Boolean algebras. As an application, the author derives a result akin to the well-known definability theorem of E. W. Beth. This new definability theorem is related to theorems of descent in category theory and algebra and can also be stated as a result in pure logic without reference to category theory. Containing novel techniques as well as applications of classical methods, this carefuly written book shows an attention to both organization and detail and will appeal to mathematicians and philosophers interested in category theory.

First-order Logic Revisited

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Author : Vincent F. Hendricks
Publisher : Logos Verlag Berlin
ISBN 13 : 9783832504755
Total Pages : 0 pages
Book Rating : 4.5/5 (47 download)

Book Synopsis First-order Logic Revisited by : Vincent F. Hendricks

Download or read book First-order Logic Revisited written by Vincent F. Hendricks and published by Logos Verlag Berlin. This book was released on 2004 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Proceedings from the conference FOL75 - 75 Years of First-Order Logic held at Humboldt University, Berlin, Germany, September 18 - 21 2003"--Pref.

First-Order Dynamic Logic

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Author : D. Harel
Publisher :
ISBN 13 : 9783662174500
Total Pages : 152 pages
Book Rating : 4.1/5 (745 download)

Book Synopsis First-Order Dynamic Logic by : D. Harel

Download or read book First-Order Dynamic Logic written by D. Harel and published by . This book was released on 2014-01-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Programming with Higher-Order Logic

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Author : Dale Miller
Publisher : Cambridge University Press
ISBN 13 : 052187940X
Total Pages : 321 pages
Book Rating : 4.5/5 (218 download)

Book Synopsis Programming with Higher-Order Logic by : Dale Miller

Download or read book Programming with Higher-Order Logic written by Dale Miller and published by Cambridge University Press. This book was released on 2012-06-11 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: A programming language based on a higher-order logic provides a declarative approach to capturing computations involving types, proofs and other syntactic structures.