Foundations of Mathematical Logic

by Haskell Brooks Curry
Foundations of Mathematical Logic
Author: Haskell Brooks Curry
Publisher: Courier Corporation
Total Pages: 420
Release: 1977-01-01
Genre: Mathematics
ISBN: 9780486634623
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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.

Lambda-Calculus and Combinators

by J. Roger Hindley
Lambda-Calculus and Combinators
Author: J. Roger Hindley
Publisher: Cambridge University Press
Total Pages: 358
Release: 2008-07-24
Genre: Computers
ISBN: 9780521898850
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Combinatory logic and lambda-calculus, originally devised in the 1920's, have since developed into linguistic tools, especially useful in programming languages. The authors' previous book served as the main reference for introductory courses on lambda-calculus for over 20 years: this long-awaited new version is thoroughly revised and offers a fully up-to-date account of the subject, with the same authoritative exposition. The grammar and basic properties of both combinatory logic and lambda-calculus are discussed, followed by an introduction to type-theory. Typed and untyped versions of the systems, and their differences, are covered. Lambda-calculus models, which lie behind much of the semantics of programming languages, are also explained in depth. The treatment is as non-technical as possible, with the main ideas emphasized and illustrated by examples. Many exercises are included, from routine to advanced, with solutions to most at the end of the book.

To Mock a Mockingbird

by Raymond M. Smullyan
To Mock a Mockingbird
Author: Raymond M. Smullyan
Publisher: Oxford University Press, USA
Total Pages: 258
Release: 2000
Genre: Games & Activities
ISBN: 0192801422
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The author of Forever Undecided, Raymond Smullyan continues to delight and astonish us with his gift for making available, in the thoroughly pleasurable form of puzzles, some of the most important mathematical thinking of our time.

Introduction to Combinators and (lambda) Calculus

by J. R. Hindley
Introduction to Combinators and (lambda) Calculus
Author: J. R. Hindley
Publisher: CUP Archive
Total Pages: 376
Release: 1986-05-29
Genre: Mathematics
ISBN: 9780521318396
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Combinatory logic and lambda-conversion were originally devised in the 1920s for investigating the foundations of mathematics using the basic concept of 'operation' instead of 'set'. They have now developed into linguistic tools, useful in several branches of logic and computer science, especially in the study of programming languages. These notes form a simple introduction to the two topics, suitable for a reader who has no previous knowledge of combinatory logic, but has taken an undergraduate course in predicate calculus and recursive functions. The key ideas and basic results are presented, as well as a number of more specialised topics, and man), exercises are included to provide manipulative practice.

Introduction to the Foundations of Mathematics

by Raymond L. Wilder
Introduction to the Foundations of Mathematics
Author: Raymond L. Wilder
Publisher: Courier Corporation
Total Pages: 354
Release: 2012-01-01
Genre: Mathematics
ISBN: 0486488209
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This classic undergraduate text by an eminent educator acquaints students with the fundamental concepts and methods of mathematics. In addition to introducing many noteworthy historical figures from the eighteenth through the mid-twentieth centuries, the book examines the axiomatic method, set theory, infinite sets, the linear continuum and the real number system, and groups. Additional topics include the Frege-Russell thesis, intuitionism, formal systems, mathematical logic, and the cultural setting of mathematics. Students and teachers will find that this elegant treatment covers a vast amount of material in a single reasonably concise and readable volume. Each chapter concludes with a set of problems and a list of suggested readings. An extensive bibliography and helpful indexes conclude the text.

The Lambda Calculus

by H.P. Barendregt
The Lambda Calculus
Author: H.P. Barendregt
Publisher: North Holland
Total Pages: 648
Release: 1984
Genre: Mathematics
ISBN:
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The revised edition contains a new chapter which provides an elegant description of the semantics. The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition. An example of a simple model is given and then the general theory (of categorical models) is developed. Indications are given of those parts of the book which can be used to form a coherent course.

The Elements of Mathematical Logic

by Paul C. Rosenbloom
The Elements of Mathematical Logic
Author: Paul C. Rosenbloom
Publisher:
Total Pages: 234
Release: 1950
Genre: Logic, Symbolic and mathematical
ISBN:
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"This book is intended for readers who, while mature mathematically, have no knowledge of mathematical logic. We attempt to introduce the reader to the most important approaches to the subject, and, wherever possible within the limitations of space which we have set for ourselves, to give at least a few nontrivial results illustrating each of the important methods for attacking logical problems"--Preface.

Combinatory Linguistics

by Cem Bozsahin
Combinatory Linguistics
Author: Cem Bozsahin
Publisher: Walter de Gruyter
Total Pages: 304
Release: 2012-12-06
Genre: Language Arts & Disciplines
ISBN: 311029687X
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The book examines to what extent the mediating relation between constituents and their semantics can arise from combinatory knowledge of words. It traces the roots of Combinatory Categorial Grammar, and uses the theory to promote a Humean question in linguistics and cognitive science: Why do we see limited constituency and dependency in natural languages, despite their diversity and potential infinity? A potential answer is that constituents and dependencies might have arisen from a single resource: adjacency. The combinatory formulation of adjacency constrains possible grammars.