Some 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.
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.
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 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.
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.
Lectures On Intuitionistic Logic Part 2
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Author :
language : en
Publisher:
Release Date : 1989
Lectures On Intuitionistic Logic Part 2 written by 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.
Intuitionistic logic has become ubiquitous in computer science. An important question is how to teach intuitionistic logic to computer science and mathematics students. We attempted to begin such an exposition in Nerode 1989 using Kripke models which allow us to represent states of knowledge about machines. This document is an introduction, without proofs, to the semantics of recursive realizability and the Curry-Howard isomorphism. This is the subject behind term extraction functional computer languages such as ML or NuPRL. Partial Contents: Orientation; Logical deduction and computation; Instuitionistic natural deduction; Heyting's semantics; Set theory and application; Curry-Howard isomorphism; Typed combinators; Second order propositional calculus; Polymorphic lambda calculus. (KR).
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
A Short Introduction To Intuitionistic Logic
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Author : Grigori Mints
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-20
A Short Introduction To Intuitionistic Logic written by Grigori Mints and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-20 with Mathematics categories.
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.
Some Lectures On Modal Logic Supplement
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Author :
language : en
Publisher:
Release Date : 1989
Some Lectures On Modal Logic Supplement written by 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.
Model logics arise throughout computer science. It is worthwhile to find the best means of exposition of theory and applications for mathematics and computer science students. The classical model logic texts are neither oriented toward computer science nor mathematics. The computational content of proof procedures and how the notions apply in computer science and AI applications has to be brought out. Here we start an exposition without proofs of propositional modal logic using a tableaux method easy to remember for hand computational and suitable for automated reasoning. The exposition is analogous to the exposition in the author's lectures on intuitionistic logic (Nerode 1990), also directed at computer science applications. Here one application exposited at length, also without proofs, is the autoepistemic logic of Moore. But any defects of exposition are solely due to present author. We outline classical constant domain modal predicate logic briefly. We conclude with dynamic logic. We give a brief introduction to a new intuitionistic dynamic logic due to D. Wijesekera, which is suitable for dealing with concurrency. (KR).