First Order Logic
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First Order Logic
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Author : Raymond R. Smullyan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
First Order Logic written by Raymond R. Smullyan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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
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Author : Leigh S. Cauman
language : en
Publisher: Walter de Gruyter
Release Date : 1998
First Order Logic written by Leigh S. Cauman and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
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
First Order Logic And Automated Theorem Proving
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Author : Melvin Fitting
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
First Order Logic And Automated Theorem Proving written by Melvin Fitting and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Extensions Of First Order Logic
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Author : Maria Manzano
language : en
Publisher: Cambridge University Press
Release Date : 1996-03-29
Extensions Of First Order Logic written by Maria Manzano and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-03-29 with Computers categories.
An introduction to many-sorted logic as an extension of first-order logic.
Metalogic
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Author : Geoffrey Hunter
language : en
Publisher: Univ of California Press
Release Date : 1973-06-26
Metalogic written by Geoffrey Hunter and has been published by Univ of California Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-06-26 with Science categories.
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.
A Philosophical Companion To First Order Logic
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Author : R. I. G. Hughes
language : en
Publisher: Hackett Publishing
Release Date : 1993
A Philosophical Companion To First Order Logic written by R. I. G. Hughes and has been published by Hackett Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Philosophy categories.
Modelling Puzzles In First Order Logic
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Author : Adrian Groza
language : en
Publisher: Springer Nature
Release Date : 2021-10-26
Modelling Puzzles In First Order Logic written by Adrian Groza and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-26 with Mathematics categories.
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 Logic
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Author : Fouad Sabry
language : en
Publisher: One Billion Knowledgeable
Release Date : 2023-06-25
First Order Logic written by Fouad Sabry and has been published by One Billion Knowledgeable this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-25 with Computers categories.
What Is First Order Logic First-order logic is a collection of formal systems that are utilized in the fields of mathematics, philosophy, linguistics, and computer science. Other names for first-order logic include predicate logic, quantificational logic, and first-order predicate calculus. In first-order logic, quantified variables take precedence over non-logical objects, and the use of sentences that contain variables is permitted. As a result, rather than making assertions like "Socrates is a man," one can make statements of the form "there exists x such that x is Socrates and x is a man," where "there exists" is a quantifier and "x" is a variable. This is in contrast to propositional logic, which does not make use of quantifiers or relations; propositional logic serves as the basis for first-order logic in this sense. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: First-order logic Chapter 2: Axiom Chapter 3: Propositional calculus Chapter 4: Peano axioms Chapter 5: Universal quantification Chapter 6: Conjunctive normal form Chapter 7: Consistency Chapter 8: Zermelo–Fraenkel set theory Chapter 9: Interpretation (logic) Chapter 10: Quantifier rank (II) Answering the public top questions about first order logic. (III) Real world examples for the usage of first order logic in many fields. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of first order logic.
First Order Mathematical Logic
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Author : Angelo Margaris
language : en
Publisher: Courier Corporation
Release Date : 1990-01-01
First Order Mathematical Logic written by Angelo Margaris and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.
"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
First Order Logic
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Author : John Heil
language : en
Publisher: Hackett Publishing
Release Date : 2021-10-06
First Order Logic written by John Heil and has been published by Hackett Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-06 with Philosophy categories.
"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