Mathematical Logic: Part 1

Propositional Calculus, Boolean Algebras, Predicate Calculus, Completeness Theorems


Author: René Cori,Daniel Lascar

Publisher: OUP Oxford

ISBN: 0191589772

Category: Mathematics

Page: 360

View: 3502

Logic forms the basis of mathematics, and is hence a fundamental part of any mathematics course. In particular, it is a major element in theoretical computer science and has undergone a huge revival with the explosion of interest in computers and computer science. This book provides students with a clear and accessible introduction to this important subject. The concept of model underlies the whole book, giving the text a theoretical coherence whilst still covering a wide area of logic.

A Course in Mathematical Logic for Mathematicians


Author: Yu. I. Manin

Publisher: Springer Science & Business Media

ISBN: 1441906150

Category: Mathematics

Page: 384

View: 872

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.

Boolean Reasoning

The Logic of Boolean Equations


Author: Frank Markham Brown

Publisher: Courier Corporation

ISBN: 0486164594

Category: Mathematics

Page: 304

View: 8147

Concise text begins with overview of elementary mathematical concepts and outlines theory of Boolean algebras; defines operators for elimination, division, and expansion; covers syllogistic reasoning, solution of Boolean equations, functional deduction. 1990 edition.

Mathematical Logic


Author: J.D. Monk

Publisher: Springer Science & Business Media

ISBN: 146849452X

Category: Mathematics

Page: 532

View: 3242

From the Introduction: "We shall base our discussion on a set-theoretical foundation like that used in developing analysis, or algebra, or topology. We may consider our task as that of giving a mathematical analysis of the basic concepts of logic and mathematics themselves. Thus we treat mathematical and logical practice as given empirical data and attempt to develop a purely mathematical theory of logic abstracted from these data." There are 31 chapters in 5 parts and approximately 320 exercises marked by difficulty and whether or not they are necessary for further work in the book.

Mathematical Logic for Computer Science


Author: Mordechai Ben-Ari

Publisher: Springer Science & Business Media

ISBN: 1447141296

Category: Mathematics

Page: 346

View: 3738

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 as Algebra


Author: Paul Halmos,Steven Givant

Publisher: Cambridge University Press

ISBN: 9780883853276

Category: Mathematics

Page: 141

View: 3829

An introduction to logic from the perspective of algebra.

Introduction to Mathematical Logic, Fourth Edition


Author: Elliott Mendelson

Publisher: CRC Press

ISBN: 9780412808302

Category: Mathematics

Page: 440

View: 5465

The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them. Introduction to Mathematical Logic includes: propositional logic first-order logic first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski axiomatic set theory theory of computability The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.

A Mathematical Introduction to Logic


Author: Herbert Enderton,Herbert B. Enderton

Publisher: Elsevier

ISBN: 0080496466

Category: Mathematics

Page: 317

View: 9144

A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets. * Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses. * Reduced mathematical rigour to fit the needs of undergraduate students

Logic Colloquium 2000

proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, held in Paris, France, July 23-31, 2000


Author: René Cori

Publisher: A K Peters Ltd


Category: Mathematics

Page: 408

View: 6690

This compilation of papers presented at the 2000 European Summer Meeting of the Association for Symbolic Logic marks the centenial anniversery of Hilbert's famous lecture. Held in the same hall at La Sorbonne where Hilbert first presented his famous problems, this meeting carries special significance to the Mathematics and Logic communities. The presentations include tutorials and research articles from some of the world's preeminent logicians. Three long articles are based on tutorials given at the meeting, and present accessible expositions of devloping research in three active areas of logic: model theory, computability, and set theory. The eleven subsequent articles cover seperate research topics in all areas of mathematical logic, including: aspects in Computer Science, Proof Theory, Set Theory, Model Theory, Computability Theory, and aspects of Philosophy.

The Elements of Mathematical Logic


Author: Paul C. Rosenbloom

Publisher: Courier Corporation

ISBN: 0486446174

Category: Mathematics

Page: 214

View: 719

This introduction to mathematical logic stresses the use of logical methods in attacking nontrivial problems. It covers the logic of classes, of propositions, of propositional functions, and the general syntax of language, with a brief introduction to so-called undecidability and incompleteness theorems; and much more. 1950 edition.

Propositional and Predicate Calculus: A Model of Argument


Author: Derek Goldrei

Publisher: Springer Science & Business Media

ISBN: 9781846282294

Category: Mathematics

Page: 315

View: 702

Designed specifically for guided independent study. Features a wealth of worked examples and exercises, many with full teaching solutions, that encourage active participation in the development of the material. It focuses on core material and provides a solid foundation for further study.

Introduction to Proof in Abstract Mathematics


Author: Andrew Wohlgemuth

Publisher: Courier Corporation

ISBN: 0486141683

Category: Mathematics

Page: 384

View: 7741

This undergraduate text teaches students what constitutes an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. 1990 edition.

Introduction to Mathematical Logic


Author: Hans Hermes

Publisher: Springer Science & Business Media

ISBN: 3642871321

Category: Mathematics

Page: 244

View: 3081

This book grew out of lectures. It is intended as an introduction to classical two-valued predicate logic. The restriction to classical logic is not meant to imply that this logic is intrinsically better than other, non-classical logics; however, classical logic is a good introduction to logic because of its simplicity, and a good basis for applications because it is the foundation of classical mathematics, and thus of the exact sciences which are based on it. The book is meant primarily for mathematics students who are already acquainted with some of the fundamental concepts of mathematics, such as that of a group. It should help the reader to see for himself the advantages of a formalisation. The step from the everyday language to a formalised language, which usually creates difficulties, is dis cussed and practised thoroughly. The analysis of the way in which basic mathematical structures are approached in mathematics leads in a natural way to the semantic notion of consequence. One of the substantial achievements of modern logic has been to show that the notion of consequence can be replaced by a provably equivalent notion of derivability which is defined by means of a calculus. Today we know of many calculi which have this property.

Discrete Structures, Logic, and Computability


Author: James L. Hein

Publisher: Jones & Bartlett Publishers

ISBN: 1284070409

Category: Computers

Page: 1050

View: 3336

Following the recent updates to the 2013 ACM/IEEE Computer Science curricula, Discrete Structures, Logic, and Computability, Fourth Edition, has been designed for the discrete math course that covers one to two semesters. Dr. Hein presents material in a spiral medthod of learning, introducing basic information about a topic, allowing the students to work on the problem and revisit the topic, as new information and skills are established. Written for prospective computer scientist, computer engineers, or applied mathematicians, who want to learn about the ideas that inspire computer science, this edition contains an extensive coverage of logic, setting it apart from similar books available in the field of Computer Science.

Proof, Logic, and Conjecture

The Mathematician's Toolbox


Author: Robert S. Wolf

Publisher: St. Martin's Press

ISBN: 9780716730507

Category: Mathematics

Page: 421

View: 9141

This text is designed to teach students how to read and write proofs in mathematics and to acquaint them with how mathematicians investigate problems and formulate conjecture.

A Course on Set Theory


Author: Ernest Schimmerling

Publisher: Cambridge University Press

ISBN: 1139501488

Category: Mathematics

Page: N.A

View: 1233

Set theory is the mathematics of infinity and part of the core curriculum for mathematics majors. This book blends theory and connections with other parts of mathematics so that readers can understand the place of set theory within the wider context. Beginning with the theoretical fundamentals, the author proceeds to illustrate applications to topology, analysis and combinatorics, as well as to pure set theory. Concepts such as Boolean algebras, trees, games, dense linear orderings, ideals, filters and club and stationary sets are also developed. Pitched specifically at undergraduate students, the approach is neither esoteric nor encyclopedic. The author, an experienced instructor, includes motivating examples and over 100 exercises designed for homework assignments, reviews and exams. It is appropriate for undergraduates as a course textbook or for self-study. Graduate students and researchers will also find it useful as a refresher or to solidify their understanding of basic set theory.

A Concise Introduction to Mathematical Logic


Author: Wolfgang Rautenberg

Publisher: Springer

ISBN: 9781441912213

Category: Mathematics

Page: 320

View: 5672

Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.

Logic and Structure


Author: Dirk van Dalen

Publisher: Springer Science & Business Media

ISBN: 3662029626

Category: Mathematics

Page: 220

View: 2151

New corrected printing of a well-established text on logic at the introductory level.

Logic for Computer Science

Foundations of Automatic Theorem Proving, Second Edition


Author: Jean H. Gallier

Publisher: Courier Dover Publications

ISBN: 0486780821

Category: Computers

Page: 528

View: 6721

This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.