Lectures On Intuitionistic Logic
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Some Lectures On Intuitionistic Logic
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Author : Anil Nerode
language : en
Publisher:
Release Date : 1989
Some Lectures On Intuitionistic Logic written by Anil Nerode and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Intuitionistic mathematics categories.
Principles Of Intuitionism
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Author : Anne S. Troelstra
language : en
Publisher: Springer
Release Date : 2006-11-14
Principles Of Intuitionism written by Anne S. Troelstra and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Lectures On Intuitionistic Logic
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Author : Anil Nerode
language : en
Publisher:
Release Date : 1989
Lectures On Intuitionistic Logic written by Anil Nerode and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
Kurt G Del
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Author : Maria Hämeen-Anttila
language : en
Publisher: Springer Nature
Release Date : 2021-12-15
Kurt G Del written by Maria Hämeen-Anttila and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-15 with Mathematics categories.
Paris of the year 1900 left two landmarks: the Tour Eiffel, and David Hilbert's celebrated list of twenty-four mathematical problems presented at a conference opening the new century. Kurt Gödel, a logical icon of that time, showed Hilbert's ideal of complete axiomatization of mathematics to be unattainable. The result, of 1931, is called Gödel's incompleteness theorem. Gödel then went on to attack Hilbert's first and second Paris problems, namely Cantor's continuum problem about the type of infinity of the real numbers, and the freedom from contradiction of the theory of real numbers. By 1963, it became clear that Hilbert's first question could not be answered by any known means, half of the credit of this seeming faux pas going to Gödel. The second is a problem still wide open. Gödel worked on it for years, with no definitive results; The best he could offer was a start with the arithmetic of the entire numbers. This book, Gödel's lectures at the famous Princeton Institute for Advanced Study in 1941, shows how far he had come with Hilbert's second problem, namely to a theory of computable functionals of finite type and a proof of the consistency of ordinary arithmetic. It offers indispensable reading for logicians, mathematicians, and computer scientists interested in foundational questions. It will form a basis for further investigations into Gödel's vast Nachlass of unpublished notes on how to extend the results of his lectures to the theory of real numbers. The book also gives insights into the conceptual and formal work that is needed for the solution of profound scientific questions, by one of the central figures of 20th century science and philosophy.
Lectures On The Curry Howard Isomorphism
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Author : Morten Heine Sørensen
language : en
Publisher: Elsevier
Release Date : 2006-07-04
Lectures On The Curry Howard Isomorphism written by Morten Heine Sørensen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-04 with Mathematics categories.
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 transformsproofs 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
Brouwer S Cambridge Lectures On Intuitionism
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Author : Luitzen Egbertus Jan Brouwer
language : en
Publisher: Cambridge University Press
Release Date : 1981
Brouwer S Cambridge Lectures On Intuitionism written by Luitzen Egbertus Jan Brouwer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
Luitzen Egburtus Jan Brouwer founded a school of thought whose aim was to include mathematics within the framework of intuitionistic philosophy; mathematics was to be regarded as an essentially free development of the human mind. What emerged diverged considerably at some points from tradition, but intuitionism has survived well the struggle between contending schools in the foundations of mathematics and exact philosophy. Originally published in 1981, this monograph contains a series of lectures dealing with most of the fundamental topics such as choice sequences, the continuum, the fan theorem, order and well-order. Brouwer's own powerful style is evident throughout the work.
Logic And Computer Science
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Author : Steven Homer
language : en
Publisher: Springer
Release Date : 2006-11-14
Logic And Computer Science written by Steven Homer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The courses given at the 1st C.I.M.E. Summer School of 1988 dealt with the main areas on the borderline between applied logic and theoretical computer science. These courses are recorded here in five expository papers: S. Homer: The Isomorphism Conjecture and its Generalization.- A. Nerode: Some Lectures on Intuitionistic Logic.- R.A. Platek: Making Computers Safe for the World. An Introduction to Proofs of Programs. Part I. - G.E. Sacks: Prolog Programming.- A. Scedrov: A Guide to Polymorphic Types.
Lectures On Linear Logic
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Author : Anne Sjerp Troelstra
language : en
Publisher: Center for the Study of Language and Information Publications
Release Date : 1992-05-01
Lectures On Linear Logic written by Anne Sjerp Troelstra and has been published by Center for the Study of Language and Information Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-01 with Mathematics categories.
The initial sections of this text deal with syntactical matters such as logical formalism, cut-elimination, and the embedding of intuitionistic logic in classical linear logic. Concluding chapters focus on proofnets for the multiplicative fragment and the algorithmic interpretation of cut-elimination in proofnets.
Lectures On Mathematical Logic
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Author : Walter Felscher
language : en
Publisher: CRC Press
Release Date : 2014-04-21
Lectures On Mathematical Logic written by Walter Felscher and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-21 with Mathematics categories.
In this volume, logic starts from the observation that in everyday arguments, as brought forward by say a lawyer, statements are transformed linguistically, connecting them in formal ways irrespective of their contents. Understanding such arguments as deductive situations, or "sequents" in the technical terminology, the transformations between them can be expressed as logical rules. The book concludes with the algorithms producing the results of Gentzen's midsequent theorem and Herbrand's theorem for prenex formulas.
Towards New Logic And Semantics
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Author : Jocelyn Benoist
language : en
Publisher:
Release Date : 2006
Towards New Logic And Semantics written by Jocelyn Benoist and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
