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A Short Introduction to Intuitionistic Logic

A Short Introduction to Intuitionistic Logic Author Grigori Mints
ISBN-10 9780306469756
Release 2006-04-11
Pages 131
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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.



Elements of Intuitionism

Elements of Intuitionism Author Michael A. E. Dummett
ISBN-10 0198505248
Release 2000
Pages 331
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This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.



Lectures on the Curry Howard Isomorphism

Lectures on the Curry Howard Isomorphism Author Morten Heine Sørensen
ISBN-10 0080478921
Release 2006-07-04
Pages 456
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The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc. The isomorphism has many aspects, even at the syntactic level: formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc. But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transforms proofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq). This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic. Key features - The Curry-Howard Isomorphism treated as common theme - Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics - Thorough study of the connection between calculi and logics - Elaborate study of classical logics and control operators - Account of dialogue games for classical and intuitionistic logic - Theoretical foundations of computer-assisted reasoning · The Curry-Howard Isomorphism treated as the common theme. · Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics. · Elaborate study of classical logics and control operators. · Account of dialogue games for classical and intuitionistic logic. · Theoretical foundations of computer-assisted reasoning



Model and Proof Theory of Constructive ALC

Model and Proof Theory of Constructive ALC Author Stephan Scheele
ISBN-10 9783863093204
Release 2015-07-02
Pages 326
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Model and Proof Theory of Constructive ALC has been writing in one form or another for most of life. You can find so many inspiration from Model and Proof Theory of Constructive ALC also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Model and Proof Theory of Constructive ALC book for free.



Mathematical Logic

Mathematical Logic Author Stephen Cole Kleene
ISBN-10 9780486317076
Release 2013-04-22
Pages 416
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Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.



Problems in Set Theory Mathematical Logic and the Theory of Algorithms

Problems in Set Theory  Mathematical Logic and the Theory of Algorithms Author Igor Lavrov
ISBN-10 9781461501855
Release 2012-12-06
Pages 282
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Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by I. Lavrov & L. Maksimova is an English translation of the fourth edition of the most popular student problem book in mathematical logic in Russian. It covers major classical topics in proof theory and the semantics of propositional and predicate logic as well as set theory and computation theory. Each chapter begins with 1-2 pages of terminology and definitions that make the book self-contained. Solutions are provided. The book is likely to become an essential part of curricula in logic.



Intuitionistic Set Theory

Intuitionistic Set Theory Author John L. Bell
ISBN-10 1848901402
Release 2014-02-28
Pages 132
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While intuitionistic (or constructive) set theory IST has received a certain attention from mathematical logicians, so far as I am aware no book providing a systematic introduction to the subject has yet been published. This may be the case in part because, as a form of higher-order intuitionistic logic - the internal logic of a topos - IST has been chiefly developed in a tops-theoretic context. In particular, proofs of relative consistency with IST for mathematical assertions have been (implicitly) formulated in topos- or sheaf-theoretic terms, rather than in the framework of Heyting-algebra-valued models, the natural extension to IST of the well-known Boolean-valued models for classical set theory. In this book I offer a brief but systematic introduction to IST which develops the subject up to and including the use of Heyting-algebra-valued models in relative consistency proofs. I believe that IST, presented as it is in the familiar language of set theory, will appeal particularly to those logicians, mathematicians and philosophers who are unacquainted with the methods of topos theory.



Handbook of Practical Logic and Automated Reasoning

Handbook of Practical Logic and Automated Reasoning Author John Harrison
ISBN-10 9780521899574
Release 2009-03-12
Pages 681
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One-stop reference, self-contained, with theoretical topics presented in conjunction with implementations for which code is supplied.



Foundations of Mathematical Logic

Foundations of Mathematical Logic Author Haskell Brooks Curry
ISBN-10 0486634620
Release 1963
Pages 408
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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.



An Introduction to the Philosophy of Mathematics

An Introduction to the Philosophy of Mathematics Author Mark Colyvan
ISBN-10 9780521826020
Release 2012-06-14
Pages 188
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This introduction to the philosophy of mathematics focuses on contemporary debates in an important and central area of philosophy. The reader is taken on a fascinating and entertaining journey through some intriguing mathematical and philosophical territory, including such topics as the realism/anti-realism debate in mathematics, mathematical explanation, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics and the applications of mathematics. Each chapter has a number of discussion questions and recommended further reading from both the contemporary literature and older sources. Very little mathematical background is assumed and all of the mathematics encountered is clearly introduced and explained using a wide variety of examples. The book is suitable for an undergraduate course in philosophy of mathematics and, more widely, for anyone interested in philosophy and mathematics.



An Introduction to Non Classical Logic

An Introduction to Non Classical Logic Author Graham Priest
ISBN-10 1139469673
Release 2008-04-10
Pages
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This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.



Classical and Nonclassical Logics

Classical and Nonclassical Logics Author Eric Schechter
ISBN-10 0691122792
Release 2005
Pages 507
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Classical logic is traditionally introduced by itself, but that makes it seem arbitrary and unnatural. This text introduces classical alongside several nonclassical logics (relevant, constructive, quantative, paraconsistent).



Knowledge Based Software Engineering

Knowledge Based Software Engineering Author M. Virvou
ISBN-10 9781607503644
Release 2008-08-15
Pages 560
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JCKBSE aims to provide a forum for researchers and practitioners to discuss the latest developments in the areas of knowledge engineering and software engineering. Particular emphasis is placed upon applying knowledge-based methods to software engineering problems.



The Bulletin of Symbolic Logic

The Bulletin of Symbolic Logic Author
ISBN-10 UVA:X030586703
Release 2009-09
Pages
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The Bulletin of Symbolic Logic has been writing in one form or another for most of life. You can find so many inspiration from The Bulletin of Symbolic Logic also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The Bulletin of Symbolic Logic book for free.



Philosophical Logic

Philosophical Logic Author John P. Burgess
ISBN-10 9781400830497
Release 2009-07-06
Pages 320
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Philosophical Logic is a clear and concise critical survey of nonclassical logics of philosophical interest written by one of the world's leading authorities on the subject. After giving an overview of classical logic, John Burgess introduces five central branches of nonclassical logic (temporal, modal, conditional, relevantistic, and intuitionistic), focusing on the sometimes problematic relationship between formal apparatus and intuitive motivation. Requiring minimal background and arranged to make the more technical material optional, the book offers a choice between an overview and in-depth study, and it balances the philosophical and technical aspects of the subject. The book emphasizes the relationship between models and the traditional goal of logic, the evaluation of arguments, and critically examines apparatus and assumptions that often are taken for granted. Philosophical Logic provides an unusually thorough treatment of conditional logic, unifying probabilistic and model-theoretic approaches. It underscores the variety of approaches that have been taken to relevantistic and related logics, and it stresses the problem of connecting formal systems to the motivating ideas behind intuitionistic mathematics. Each chapter ends with a brief guide to further reading. Philosophical Logic addresses students new to logic, philosophers working in other areas, and specialists in logic, providing both a sophisticated introduction and a new synthesis.



BPR

BPR Author
ISBN-10 STANFORD:36105111050477
Release 2000-07
Pages
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BPR has been writing in one form or another for most of life. You can find so many inspiration from BPR also informative, and entertaining. Click DOWNLOAD or Read Online button to get full BPR book for free.



Logical Options

Logical Options Author John L. Bell
ISBN-10 9781551112978
Release 2001-03-30
Pages 300
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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.