Logic for Mathematicians


Author: A. G. Hamilton
Publisher: Cambridge University Press
ISBN: 9780521368650
Category: Mathematics
Page: 228
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This is an introductory textbook which is designed to be useful not only to intending logicians but also to mathematicians in general.

A Course in Mathematical Logic for Mathematicians


Author: Yu. I. Manin
Publisher: Springer Science & Business Media
ISBN: 1441906150
Category: Mathematics
Page: 384
View: 4843

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1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.

Logic for Mathematicians


Author: J. Barkley Rosser
Publisher: Courier Dover Publications
ISBN: 0486468984
Category: Mathematics
Page: 574
View: 7101

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Hailed by the Bulletin of the American Mathematical Society as "undoubtedly a major addition to the literature of mathematical logic," this volume examines the essential topics and theorems of mathematical reasoning. No background in logic is assumed, and the examples are chosen from a variety of mathematical fields. Starting with an introduction to symbolic logic, the first eight chapters develop logic through the restricted predicate calculus. Topics include the statement calculus, the use of names, an axiomatic treatment of the statement calculus, descriptions, and equality. Succeeding chapters explore abstract set theory—with examinations of class membership as well as relations and functions—cardinal and ordinal arithmetic, and the axiom of choice. An invaluable reference book for all mathematicians, this text is suitable for advanced undergraduates and graduate students. Numerous exercises make it particularly appropriate for classroom use.

Numbers, Sets and Axioms

The Apparatus of Mathematics
Author: A. G. Hamilton
Publisher: Cambridge University Press
ISBN: 9780521287616
Category: Mathematics
Page: 255
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Following the success of Logic for Mathematicians, Dr Hamilton has written a text for mathematicians and students of mathematics that contains a description and discussion of the fundamental conceptual and formal apparatus upon which modern pure mathematics relies. The author's intention is to remove some of the mystery that surrounds the foundations of mathematics. He emphasises the intuitive basis of mathematics; the basic notions are numbers and sets and they are considered both informally and formally. The role of axiom systems is part of the discussion but their limitations are pointed out. Formal set theory has its place in the book but Dr Hamilton recognises that this is a part of mathematics and not the basis on which it rests. Throughout, the abstract ideas are liberally illustrated by examples so this account should be well-suited, both specifically as a course text and, more broadly, as background reading. The reader is presumed to have some mathematical experience but no knowledge of mathematical logic is required.

Logic for Programming, Artificial Intelligence, and Reasoning

18th International Conference, LPAR-18, Merida, Venezuela, March 11-15, 2012, Proceedings
Author: Nikolaj Bjørner,Andrei Voronkov
Publisher: Springer
ISBN: 3642287174
Category: Computers
Page: 446
View: 4841

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This book constitutes the proceedings of the 18th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR-18, held in Merida, Venezuela, in March 2012. The 25 regular papers and 6 tool descriptions and experimental papers presented were carefully reviewed and selected from 74 submissions. The series of International Conferences on Logic for Programming, Artificial Intelligence and Reasoning (LPAR) is a forum where, year after year, some of the most renowned researchers in the areas of logic, automated reasoning, computational logic, programming languages and their applications come to present cutting-edge results, to discuss advances in these fields, and to exchange ideas in a scientifically emerging part of the world.

Logic for Applications


Author: Anil Nerode,Richard Shore
Publisher: Springer Science & Business Media
ISBN: 9780387948935
Category: Computers
Page: 456
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In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the re cent dramatic growth in the applications oflogic to computer science. Thus, our choice oftopics has been heavily influenced by such applications. Of course, we cover the basic traditional topics: syntax, semantics, soundnes5, completeness and compactness as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much ofour book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic especially in its application to Logic Programming and PRO LOG. We deal extensively with the mathematical foundations ofall three ofthese subjects. In addition, we include two chapters on nonclassical logics - modal and intuitionistic - that are becoming increasingly important in computer sci ence. We develop the basic material on the syntax and semantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method in troduced for classical logic. We indicate how it can easily be adapted to various other special types of modal logics. A number of more advanced topics (includ ing nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.

Logic for Mathematics and Computer Science


Author: Stanley Burris
Publisher: Pearson College Division
ISBN: N.A
Category: Computers
Page: 420
View: 2112

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This book provides an elementary "hands-on" presentation of important mathematical logic topics.Explores topics that are at the cutting edge of developments in computer science, while preserving the integrity of traditional logic. Stresses several self-contained proof systems of interest to mathematical logic, some more suitable than others for particular kinds of questions. For anyone interested in Computer Science or Mathematics.

The Oxford Handbook of Philosophy of Mathematics and Logic


Author: Stewart Shapiro
Publisher: Oxford University Press
ISBN: 0190287535
Category: Mathematics
Page: 856
View: 9277

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Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.

Mathematical Logic for Computer Science


Author: Mordechai Ben-Ari
Publisher: Springer Science & Business Media
ISBN: 1447141296
Category: Mathematics
Page: 346
View: 5924

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Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of students of computer science. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and easy to understand. The uniform use of tableaux-based techniques facilitates learning advanced logical systems based on what the student has learned from elementary systems. The logical systems presented are: propositional logic, first-order logic, resolution and its application to logic programming, Hoare logic for the verification of sequential programs, and linear temporal logic for the verification of concurrent programs. The third edition has been entirely rewritten and includes new chapters on central topics of modern computer science: SAT solvers and model checking.

Logic: a Brief Course


Author: Daniele Mundici
Publisher: Springer Science & Business Media
ISBN: 9788847023611
Category: Mathematics
Page: 130
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This short book, geared towards undergraduate students of computer science and mathematics, is specifically designed for a first course in mathematical logic. A proof of Gödel's completeness theorem and its main consequences is given using Robinson's completeness theorem and Gödel's compactness theorem for propositional logic. The reader will familiarize himself with many basic ideas and artifacts of mathematical logic: a non-ambiguous syntax, logical equivalence and consequence relation, the Davis-Putnam procedure, Tarski semantics, Herbrand models, the axioms of identity, Skolem normal forms, nonstandard models and, interestingly enough, proofs and refutations viewed as graphic objects. The mathematical prerequisites are minimal: the book is accessible to anybody having some familiarity with proofs by induction. Many exercises on the relationship between natural language and formal proofs make the book also interesting to a wide range of students of philosophy and linguistics.

Einführung in die symbolische Logik

mit besonderer Berücksichtigung ihrer Anwendungen
Author: Rudolf Carnap
Publisher: Springer-Verlag
ISBN: 3709135346
Category: Philosophy
Page: 209
View: 1449

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In der Gestalt der symbolischen oder mathematischen Logik oder Logistik hat die Logik seit etwa 100 Jahren eine völlig neue Form an genommen. Die Verwendung von Symbolen ist zwar das auffallendste Merkmal der neuen Logik, aber nicht das wesentlichste. Wichtiger sind die Exaktheit der Formulierung, die große Ausdehnung des Gebietes, ins besondere in der Theorie der Relationen und der Begriffe höherer Stufen, und die vielfältige Anwendungsmöglichkeit der neuen Methoden. In den letzten Jahrzehnten ist daher das Interesse an der symbolischen Logik in weiteren Kreisen wachgeworden, besonders unter Philosophen und Mathematikern, aber auch unter den Fachwissenschaftlern, die an der Analyse der Begriffe ihrer Fachwissenschaften interessiert sind. Ins besondere in den Vereinigten Staaten ist die symbolische Logik heute ein anerkanntes Fachgebiet in Forschung und Unterricht; hier betrachten die meisten Autoren, die über Philosophie der Erkenntnis, Sprachanalyse, Methodenlehre der Wissenschaft, Grundlagen der Mathematik, axioma. tische Methode und ähnliches schreiben, die symbolische Logik als ein unentbehrliches Hilfsmittel. Dieses Buch möchte dazu beitragen, das Interesse an der symbolischen Logik in den deutschsprachigen Ländern zu fördern. Es unterscheidet sich von den übrigen Lehrbüchern, die meist in englischer Sprache erschienen sind, hauptsächlich in folgenden Punkten. Hier werden nicht nur, wie sonst üblich, die elementaren Teile der Theorie dargestellt, sondern auch ausführlich die höheren Gebiete, besonders die Logik der Relationen, die für die Anwendung besonders wichtig sind. Ferner ist der ganze Teil II der Anwendung der symbolischen Logik gewidmet.

Foundations of Mathematical Logic


Author: Haskell Brooks Curry
Publisher: Courier Corporation
ISBN: 9780486634623
Category: Mathematics
Page: 408
View: 6056

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Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods — including algorithms and epitheory — and offers a brief treatment of Markov's approach to algorithms. It also explains elementary facts about lattices and similar algebraic systems. 1963 edition.

Atomic Physics: 8th Edition


Author: Max Born
Publisher: Courier Corporation
ISBN: 0486318583
Category: Science
Page: 544
View: 9950

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Nobel Laureate's lucid treatment of kinetic theory of gases, elementary particles, nuclear atom, wave-corpuscles, atomic structure and spectral lines, much more. Over 40 appendices, bibliography.

Non-Linear Elastic Deformations


Author: R. W. Ogden
Publisher: Courier Corporation
ISBN: 0486318710
Category: Technology & Engineering
Page: 544
View: 6768

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Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.

An Introduction to the Theory of Elasticity


Author: R. J. Atkin,N. Fox
Publisher: Courier Corporation
ISBN: 0486150992
Category: Science
Page: 272
View: 2611

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Accessible text covers deformation and stress, derivation of equations of finite elasticity, and formulation of infinitesimal elasticity with application to two- and three-dimensional static problems and elastic waves. 1980 edition.

An Introduction to Differential Geometry


Author: T. J. Willmore
Publisher: Courier Corporation
ISBN: 0486282104
Category: Mathematics
Page: 336
View: 1651

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This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.

Mathematics and Logic


Author: Mark Kac,Stanislaw M. Ulam
Publisher: Courier Corporation
ISBN: 0486670856
Category: Philosophy
Page: 170
View: 8178

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Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."

Mathematics of the 19th Century

Mathematical Logic, Algebra, Number Theory, Probability Theory
Author: Andreĭ Nikolaevich Kolmogorov,Adolʹf Pavlovich I͡Ushkevich
Publisher: Springer Science & Business Media
ISBN: 9783764364410
Category: Mathematics
Page: 308
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New Edition - New in Paperback - This is the second revised edition of the first volume of the outstanding collection of historical studies of mathematics in the nineteenth century compiled in three volumes by A. N. Kolmogorov and A. P. Yushkevich. This second edition was carefully revised by Abe Shenitzer, York University, Ontario, Canada. The historical period covered in this book extends from the early nineteenth century up to the end of the 1930s, as neither 1801 nor 1900 are, in themselves, turning points in the history of mathematics, although each date is notable fo a remarkable event: the first for the publication of Gauss' "Disquisitiones arithmeticae," the second for Hilbert's "Mathematical Problems." Beginning in the second quarter of the nineteenth century mathematics underwent a revolution as crucial and profound in its consequences for the general world outlook as the mathematical revolution in the beginning of the modern era. The main changes included a new statement of the problem of the existence of mathematical objects, particulary in the calculus, and soon thereafter the formation of non-standard structures in geometry, arithmetic and algebra. The primary objective of the work has been to treat the evolution of mathematics in the nineteenth century as a whole; the discussion is concentrated on the essential concepts, methods, and algorithms.

Empiricism, Logic and Mathematics

Philosophical Papers
Author: Hans Hahn
Publisher: Springer Science & Business Media
ISBN: 9400989822
Category: Science
Page: 142
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The role Hans Hahn played in the Vienna Circle has not always been sufficiently appreciated. It was important in several ways. In the ftrst place, Hahn belonged to the trio of the original planners of the Circle. As students at the University of Vienna and throughout the fIrst decade of this century, he and his friends, Philipp Frank and Otto Neurath, met more or less regularly to discuss philosophical questions. When Hahn accepted his fIrSt professorial position, at the University of Czernowitz in the north east of the Austrian empire, and the paths of the three friends parted, they decided to continue such informal discussions at some future time - perhaps in a somewhat larger group and with the cooperation of a philosopher from the university. Various events delayed the execution of the project. Drafted into the Austrian army during the first world war" Hahn was wounded on the Italian front. Toward the end of the war he accepted an offer from the University of Bonn extended in recognition of his remarkable 1 mathematical achievements. He remained in Bonn until the spring of 1921 when he returm:d to Vienna and a chair of mathe matics at his alma mater. There, in 1922, the Mach-Boltzmann professorship for the philosophy of the inductive sciences became vacant by the death of Adolf Stohr; and Hahn saw a chance to realize his and his friends' old plan.

Principia Mathematica.


Author: Alfred North Whitehead,Bertrand Russell
Publisher: N.A
ISBN: N.A
Category: Logic, Symbolic and mathematical
Page: 167
View: 1446

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