First Order Logic

Author : Raymond R. Smullyan
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642867187

Get Book

First-Order Logic by Raymond R. Smullyan Pdf

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).

Author : Maria Manzano
Publisher : Cambridge University Press
Page : 414 pages
File Size : 51,5 Mb
Release : 1996-03-29
Category : Computers
ISBN : 0521354358

Get Book

Extensions of First-Order Logic by Maria Manzano Pdf

An introduction to many-sorted logic as an extension of first-order logic.

Author : Melvin Fitting
Publisher : Springer Science & Business Media
Page : 258 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468403572

Get Book

First-Order Logic and Automated Theorem Proving by Melvin Fitting Pdf

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.

Author : Craig DeLancey
Publisher : Open SUNY Textbooks
Page : 128 pages
File Size : 46,6 Mb
Release : 2017-02-06
Category : Electronic
ISBN : 1942341431

Get Book

A Concise Introduction to Logic by Craig DeLancey Pdf

Author : Geoffrey Hunter
Publisher : Univ of California Press
Page : 306 pages
File Size : 48,8 Mb
Release : 1973-06-26
Category : Mathematics
ISBN : 0520023560

Get Book

Metalogic by Geoffrey Hunter Pdf

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.

Author : Adrian Groza
Publisher : Springer Nature
Page : 344 pages
File Size : 54,7 Mb
Release : 2021-10-26
Category : Mathematics
ISBN : 9783030625474

Get Book

Modelling Puzzles in First Order Logic by Adrian Groza Pdf

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.

Author : John Heil
Publisher : Hackett Publishing
Page : 303 pages
File Size : 49,5 Mb
Release : 2021-10-06
Category : Philosophy
ISBN : 9781647920104

Get Book

First-Order Logic by John Heil Pdf

"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

Author : Leigh S. Cauman
Publisher : Walter de Gruyter
Page : 356 pages
File Size : 55,6 Mb
Release : 1998
Category : Mathematics
ISBN : 3110157667

Get Book

First-order Logic by Leigh S. Cauman Pdf

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

Author : M. Makkai,G.E. Reyes
Publisher : Springer
Page : 317 pages
File Size : 43,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540371007

Get Book

First Order Categorical Logic by M. Makkai,G.E. Reyes Pdf

Author : M. Fitting,Richard L. Mendelsohn
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Philosophy
ISBN : 9789401152921

Get Book

First-Order Modal Logic by M. Fitting,Richard L. Mendelsohn Pdf

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.

Author : Angelo Margaris
Publisher : Courier Corporation
Page : 244 pages
File Size : 50,8 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 0486662691

Get Book

First Order Mathematical Logic by Angelo Margaris Pdf

"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

Author : J. Lambek,P. J. Scott
Publisher : Cambridge University Press
Page : 308 pages
File Size : 47,8 Mb
Release : 1988-03-25
Category : Mathematics
ISBN : 0521356539

Get Book

Introduction to Higher-Order Categorical Logic by J. Lambek,P. J. Scott Pdf

Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.

Author : Kenneth Kunen
Publisher : Unknown
Page : 251 pages
File Size : 51,5 Mb
Release : 2009
Category : Mathematics
ISBN : 1904987141

Get Book

The Foundations of Mathematics by Kenneth Kunen Pdf

Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.

Author : D. Harel
Publisher : Unknown
Page : 152 pages
File Size : 45,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662174502

Get Book

First-Order Dynamic Logic by D. Harel Pdf

Author : Vincent F. Hendricks
Publisher : Logos Verlag Berlin
Page : 0 pages
File Size : 47,9 Mb
Release : 2004
Category : First-order logic
ISBN : 3832504753

Get Book

First-order Logic Revisited by Vincent F. Hendricks Pdf

"Proceedings from the conference FOL75 - 75 Years of First-Order Logic held at Humboldt University, Berlin, Germany, September 18 - 21 2003"--Pref.