A Short Introduction To Intuitionistic Logic

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A Short Introduction to Intuitionistic Logic

Author : Grigori Mints
Publisher : Springer Science & Business Media
ISBN 13 : 0306469758
Total Pages : 130 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis A Short Introduction to Intuitionistic Logic by : Grigori Mints

Download or read book A Short Introduction to Intuitionistic Logic written by Grigori Mints and published by Springer Science & Business Media. This book was released on 2005-12-20 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs. to make the material more accessible, basic techniques are presented first for propositional logic; Part II contains extensions to predicate logic. This material provides an introduction and a safe background for reading research literature in logic and computer science as well as advanced monographs. Readers are assumed to be familiar with basic notions of first order logic. One device for making this book short was inventing new proofs of several theorems. The presentation is based on natural deduction. The topics include programming interpretation of intuitionistic logic by simply typed lambda-calculus (Curry-Howard isomorphism), negative translation of classical into intuitionistic logic, normalization of natural deductions, applications to category theory, Kripke models, algebraic and topological semantics, proof-search methods, interpolation theorem. The text developed from materal for several courses taught at Stanford University in 1992-1999.

A Short Introduction to Intuitionistic Logic

Author : Grigori Mints
Publisher : Springer Science & Business Media
ISBN 13 : 0306463946
Total Pages : 130 pages
Book Rating : 4.3/5 (64 download)

DOWNLOAD NOW!

Book Synopsis A Short Introduction to Intuitionistic Logic by : Grigori Mints

Download or read book A Short Introduction to Intuitionistic Logic written by Grigori Mints and published by Springer Science & Business Media. This book was released on 2000-10-31 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs to make the material more accessible. The presentation is based on natural deduction and readers are assumed to be familiar with basic notions of first order logic.

Philosophical and Mathematical Logic

Author : Harrie de Swart
Publisher : Springer
ISBN 13 : 3030032558
Total Pages : 558 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Philosophical and Mathematical Logic by : Harrie de Swart

Download or read book Philosophical and Mathematical Logic written by Harrie de Swart and published by Springer. This book was released on 2018-11-28 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was written to serve as an introduction to logic, with in each chapter – if applicable – special emphasis on the interplay between logic and philosophy, mathematics, language and (theoretical) computer science. The reader will not only be provided with an introduction to classical logic, but to philosophical (modal, epistemic, deontic, temporal) and intuitionistic logic as well. The first chapter is an easy to read non-technical Introduction to the topics in the book. The next chapters are consecutively about Propositional Logic, Sets (finite and infinite), Predicate Logic, Arithmetic and Gödel’s Incompleteness Theorems, Modal Logic, Philosophy of Language, Intuitionism and Intuitionistic Logic, Applications (Prolog; Relational Databases and SQL; Social Choice Theory, in particular Majority Judgment) and finally, Fallacies and Unfair Discussion Methods. Throughout the text, the author provides some impressions of the historical development of logic: Stoic and Aristotelian logic, logic in the Middle Ages and Frege's Begriffsschrift, together with the works of George Boole (1815-1864) and August De Morgan (1806-1871), the origin of modern logic. Since "if ..., then ..." can be considered to be the heart of logic, throughout this book much attention is paid to conditionals: material, strict and relevant implication, entailment, counterfactuals and conversational implicature are treated and many references for further reading are given. Each chapter is concluded with answers to the exercises. Philosophical and Mathematical Logic is a very recent book (2018), but with every aspect of a classic. What a wonderful book! Work written with all the necessary rigor, with immense depth, but without giving up clarity and good taste. Philosophy and mathematics go hand in hand with the most diverse themes of logic. An introductory text, but not only that. It goes much further. It's worth diving into the pages of this book, dear reader! Paulo Sérgio Argolo

The Boundary Stones of Thought

Author : Ian Rumfitt
Publisher :
ISBN 13 : 0198733631
Total Pages : 369 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis The Boundary Stones of Thought by : Ian Rumfitt

Download or read book The Boundary Stones of Thought written by Ian Rumfitt and published by . This book was released on 2015 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical logic has been attacked by adherents of rival, anti-realist logical systems: Ian Rumfitt comes to its defence. He considers the nature of logic, and how to arbitrate between different logics. He argues that classical logic may dispense with the principle of bivalence, and may thus be liberated from the dead hand of classical semantics.

Treatise on Intuitionistic Type Theory

Author : Johan Georg Granström
Publisher : Springer Science & Business Media
ISBN 13 : 9400717369
Total Pages : 198 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Treatise on Intuitionistic Type Theory by : Johan Georg Granström

Download or read book Treatise on Intuitionistic Type Theory written by Johan Georg Granström and published by Springer Science & Business Media. This book was released on 2011-06-02 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.

A Logical Foundation for Potentialist Set Theory

Author : Sharon Berry
Publisher : Cambridge University Press
ISBN 13 : 1108834310
Total Pages : 249 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis A Logical Foundation for Potentialist Set Theory by : Sharon Berry

Download or read book A Logical Foundation for Potentialist Set Theory written by Sharon Berry and published by Cambridge University Press. This book was released on 2022-02-17 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to the standard axioms of set theory, relating the theory to the philosophy of science and metametaphysics.

Logical Options

Author : John L. Bell
Publisher : Broadview Press
ISBN 13 : 1551112973
Total Pages : 313 pages
Book Rating : 4.5/5 (511 download)

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Book Synopsis Logical Options by : John L. Bell

Download or read book Logical Options written by John L. Bell and published by Broadview Press. This book was released on 2001-03-30 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some classical first-order logic and would like to learn about other logics important to their philosophical work.

Logical Foundations of Computer Science

Author : Sergei Artemov
Publisher : Springer
ISBN 13 : 3540727345
Total Pages : 522 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Logical Foundations of Computer Science by : Sergei Artemov

Download or read book Logical Foundations of Computer Science written by Sergei Artemov and published by Springer. This book was released on 2007-06-30 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2007, held in New York, NY, USA in June 2007. The volume presents 36 revised refereed papers that address all current aspects of logic in computer science.

Mathematical Logic and Computation

Author : Jeremy Avigad
Publisher : Cambridge University Press
ISBN 13 : 1108478751
Total Pages : 527 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Mathematical Logic and Computation by : Jeremy Avigad

Download or read book Mathematical Logic and Computation written by Jeremy Avigad and published by Cambridge University Press. This book was released on 2022-09-30 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough introduction to the fundamental methods and results in mathematical logic, and its foundational role in computer science.

Logic and Structure

Author : Dirk van Dalen
Publisher : Springer Science & Business Media
ISBN 13 : 1447145585
Total Pages : 267 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Logic and Structure by : Dirk van Dalen

Download or read book Logic and Structure written by Dirk van Dalen and published by Springer Science & Business Media. This book was released on 2012-11-13 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dirk van Dalen’s popular textbook Logic and Structure, now in its fifth edition, provides a comprehensive introduction to the basics of classical and intuitionistic logic, model theory and Gödel’s famous incompleteness theorem. Propositional and predicate logic are presented in an easy-to-read style using Gentzen’s natural deduction. The book proceeds with some basic concepts and facts of model theory: a discussion on compactness, Skolem-Löwenheim, non-standard models and quantifier elimination. The discussion of classical logic is concluded with a concise exposition of second-order logic. In view of the growing recognition of constructive methods and principles, intuitionistic logic and Kripke semantics is carefully explored. A number of specific constructive features, such as apartness and equality, the Gödel translation, the disjunction and existence property are also included. The last chapter on Gödel's first incompleteness theorem is self-contained and provides a systematic exposition of the necessary recursion theory. This new edition has been properly revised and contains a new section on ultra-products.

Logic and Structure

Author : Dirk van Dalen
Publisher : Springer Science & Business Media
ISBN 13 : 3662023822
Total Pages : 218 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Logic and Structure by : Dirk van Dalen

Download or read book Logic and Structure written by Dirk van Dalen and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: New corrected printing of a well-established text on logic at the introductory level.

Mathematical Logic

Author : J.D. Monk
Publisher : Springer Science & Business Media
ISBN 13 : 146849452X
Total Pages : 535 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Mathematical Logic by : J.D. Monk

Download or read book Mathematical Logic written by J.D. Monk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Logics in Artificial Intelligence

Author : Francesco Calimeri
Publisher : Springer
ISBN 13 : 3030195708
Total Pages : 825 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Logics in Artificial Intelligence by : Francesco Calimeri

Download or read book Logics in Artificial Intelligence written by Francesco Calimeri and published by Springer. This book was released on 2019-05-06 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 16th European Conference on Logics in Artificial Intelligence, JELIA 2019, held in Rende, Italy, in May 2019. The 50 full papers and 10 short papers included in this volume were carefully reviewed and selected from 101 submissions. Additionally, the book contains 3 invited papers. The accepted papers span a number of areas within Logics in AI, including: belief revision and argumentation; causal, defeasible and inductive reasoning; conditional, probabilistic and propositional logic; description logics; logic programming; modal and default logic; and temporal logic.

Proof Technology and Computation

Author : Helmut Schwichtenberg
Publisher : IOS Press
ISBN 13 : 1586036254
Total Pages : 456 pages
Book Rating : 4.5/5 (86 download)

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Book Synopsis Proof Technology and Computation by : Helmut Schwichtenberg

Download or read book Proof Technology and Computation written by Helmut Schwichtenberg and published by IOS Press. This book was released on 2006 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proof technology aims at integrating proof processing into industrial design and verifications tools. The chapters in this book deal with: the benefits and technical challenges of sharing formal mathematics among interactive theorem provers; proof normalization for various axiomatic theories; and more.

Handbook of Philosophical Logic

Author : Dov M. Gabbay
Publisher : Springer Science & Business Media
ISBN 13 : 9400952031
Total Pages : 527 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Handbook of Philosophical Logic by : Dov M. Gabbay

Download or read book Handbook of Philosophical Logic written by Dov M. Gabbay and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a number of systems of logic which can be considered as alternatives to classical logic. The notion of what counts as an alternative is a somewhat problematic one. There are extreme views on the matter of what is the 'correct' logical system and whether one logical system (e. g. classical logic) can represent (or contain) all the others. The choice of the systems presented in this volume was guided by the following criteria for including a logic as an alternative: (i) the departure from classical logic in accepting or rejecting certain theorems of classical logic following intuitions arising from significant application areas and/or from human reasoning; (ii) the alternative logic is well-established and well-understood mathematically and is widely applied in other disciplines such as mathematics, physics, computer science, philosophy, psychology, or linguistics. A number of other alternatives had to be omitted for the present volume (e. g. recent attempts to formulate so-called 'non-monotonic' reason ing systems). Perhaps these can be included in future extensions of the Handbook of Philosophical Logic. Chapter 1 deals with partial logics, that is, systems where sentences do not always have to be either true or false, and where terms do not always have to denote. These systems are thus, in general, geared towards reasoning in partially specified models. Logics of this type have arisen mainly from philo sophical and linguistic considerations; various applications in theoretical computer science have also been envisaged.

Handbook of Practical Logic and Automated Reasoning

Author : John Harrison
Publisher : Cambridge University Press
ISBN 13 : 0521899575
Total Pages : 703 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Handbook of Practical Logic and Automated Reasoning by : John Harrison

Download or read book Handbook of Practical Logic and Automated Reasoning written by John Harrison and published by Cambridge University Press. This book was released on 2009-03-12 with total page 703 pages. Available in PDF, EPUB and Kindle. Book excerpt: A one-stop reference, self-contained, with theoretical topics presented in conjunction with implementations for which code is supplied.

Innovations in Defence Support Systems - 2

Author : Lakhmi C Jain
Publisher : Springer
ISBN 13 : 3642177646
Total Pages : 297 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Innovations in Defence Support Systems - 2 by : Lakhmi C Jain

Download or read book Innovations in Defence Support Systems - 2 written by Lakhmi C Jain and published by Springer. This book was released on 2011-02-05 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Innovations in Defence Support Systems - 2 presents a sample of the state-of-art research on defence support systems. The focus of the volume is on the design and optimization of socio-technical systems and their performance in defence contexts. Conceptual and methodological considerations for the development of such systems and criteria likely to be useful in their evaluation are discussed, along with their conceptual underpinnings in total system performance analysis.