Intuitionism And Proof Theory
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Mathematical Intuitionism Introduction To Proof Theory
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Author : Al'bert Grigor'evi_ Dragalin
language : en
Publisher: American Mathematical Soc.
Release Date : 1988-12-31
Mathematical Intuitionism Introduction To Proof Theory written by Al'bert Grigor'evi_ Dragalin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-12-31 with Mathematics categories.
In the area of mathematical logic, a great deal of attention is now being devoted to the study of nonclassical logics. This book intends to present the most important methods of proof theory in intuitionistic logic and to acquaint the reader with the principal axiomatic theories based on intuitionistic logic.
Intuitionism And Proof Theory Proceedings Of The Summer Conference At Buffalo N Y 1968
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Author : Lev D. Beklemishev
language : en
Publisher: Elsevier
Release Date : 2000-04-01
Intuitionism And Proof Theory Proceedings Of The Summer Conference At Buffalo N Y 1968 written by Lev D. Beklemishev and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Computers categories.
Intuitionism and Proof Theory: Proceedings of the Summer Conference at Buffalo N.Y. 1968
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.
Proof Methods For Modal And Intuitionistic Logics
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Author : M. Fitting
language : en
Publisher: Springer Science & Business Media
Release Date : 1983-04-30
Proof Methods For Modal And Intuitionistic Logics written by M. Fitting 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 1983-04-30 with Mathematics categories.
"Necessity is the mother of invention. " Part I: What is in this book - details. There are several different types of formal proof procedures that logicians have invented. The ones we consider are: 1) tableau systems, 2) Gentzen sequent calculi, 3) natural deduction systems, and 4) axiom systems. We present proof procedures of each of these types for the most common normal modal logics: S5, S4, B, T, D, K, K4, D4, KB, DB, and also G, the logic that has become important in applications of modal logic to the proof theory of Peano arithmetic. Further, we present a similar variety of proof procedures for an even larger number of regular, non-normal modal logics (many introduced by Lemmon). We also consider some quasi-regular logics, including S2 and S3. Virtually all of these proof procedures are studied in both propositional and first-order versions (generally with and without the Barcan formula). Finally, we present the full variety of proof methods for Intuitionistic logic (and of course Classical logic too). We actually give two quite different kinds of tableau systems for the logics we consider, two kinds of Gentzen sequent calculi, and two kinds of natural deduction systems. Each of the two tableau systems has its own uses; each provides us with different information about the logics involved. They complement each other more than they overlap. Of the two Gentzen systems, one is of the conventional sort, common in the literature.
Mathematical Intuitionism
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Author : Alʹbert Grigorʹevich Dragalin
language : en
Publisher:
Release Date : 1988
Mathematical Intuitionism written by Alʹbert Grigorʹevich Dragalin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Intuitionistic mathematics categories.
This monograph is intended to present the most important methods of proof theory in intuitionistic logic, assuming the reader to have mastered an introductory course in mathematical logic. The book starts with purely syntactical methods based on Gentzen's cut-elimination theorem, followed by intuitionistic arithmetic where Kleene's realizability method plays a central role. The author then studies algebraic models and completeness theorems for them. After giving a survey on the principles of intuitionistic analysis, the last part of the book presents the cut-elimination theorem in intuitionist.
Proof Theory
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Author : K. Schütte
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Proof Theory written by K. Schütte 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 2012-12-06 with Mathematics categories.
This book was originally intended to be the second edition of the book "Beweis theorie" (Grundlehren der mathematischen Wissenschaften, Band 103, Springer 1960), but in fact has been completely rewritten. As well as classical predicate logic we also treat intuitionistic predicate logic. The sentential calculus properties of classical formal and semiformal systems are treated using positive and negative parts of formulas as in the book "Beweistheorie". In a similar way we use right and left parts of formulas for intuitionistic predicate logic. We introduce the theory of functionals of finite types in order to present the Gi:idel interpretation of pure number theory. Instead of ramified type theory, type-free logic and the associated formalization of parts of analysis which we treated in the book "Beweistheorie", we have developed simple classical type theory and predicative analysis in a systematic way. Finally we have given consistency proofs for systems of lI~-analysis following the work of G. Takeuti. In order to do this we have introduced a constni'ctive system of notation for ordinals which goes far beyond the notation system in "Beweistheorie."
Proof Theory
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Author : Wolfram Pohlers
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-01
Proof Theory written by Wolfram Pohlers 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 2008-10-01 with Mathematics categories.
The kernel of this book consists of a series of lectures on in?nitary proof theory which I gave during my time at the Westfalische ̈ Wilhelms–Universitat ̈ in Munster ̈ . It was planned as a successor of Springer Lecture Notes in Mathematics 1407. H- ever, when preparing it, I decided to also include material which has not been treated in SLN 1407. Since the appearance of SLN 1407 many innovations in the area of - dinal analysis have taken place. Just to mention those of them which are addressed in this book: Buchholz simpli?ed local predicativity by the invention of operator controlled derivations (cf. Chapter 9, Chapter 11); Weiermann detected applications of methods of impredicative proof theory to the characterization of the provable recursive functions of predicative theories (cf. Chapter 10); Beckmann improved Gentzen’s boundedness theorem (which appears as Stage Theorem (Theorem 6. 6. 1) in this book) to Theorem 6. 6. 9, a theorem which is very satisfying in itself - though its real importance lies in the ordinal analysis of systems, weaker than those treated here. Besides these innovations I also decided to include the analysis of the theory (? –REF) as an example of a subtheory of set theory whose ordinal analysis only 2 0 requires a ?rst step into impredicativity. The ordinal analysis of(? –FXP) of non- 0 1 0 monotone? –de?nable inductive de?nitions in Chapter 13 is an application of the 1 analysis of(? –REF).
The Good In The Right
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Author : Robert Audi
language : en
Publisher:
Release Date : 2004
The Good In The Right written by Robert Audi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Philosophy categories.
This book represents the most comprehensive account to date of an important but widely contested approach to ethics--intuitionism, the view that there is a plurality of moral principles, each of which we can know directly. Robert Audi casts intuitionism in a form that provides a major alternative to the more familiar ethical perspectives (utilitarian, Kantian, and Aristotelian). He introduces intuitionism in its historical context and clarifies--and improves and defends--W. D. Ross's influential formulation. Bringing Ross out from under the shadow of G. E. Moore, he puts a reconstructed version of Rossian intuitionism on the map as a full-scale, plausible contemporary theory. A major contribution of the book is its integration of Rossian intuitionism with Kantian ethics; this yields a view with advantages over other intuitionist theories (including Ross's) and over Kantian ethics taken alone. Audi proceeds to anchor Kantian intuitionism in a pluralistic theory of value, leading to an account of the perennially debated relation between the right and the good. Finally, he sets out the standards of conduct the theory affirms and shows how the theory can help guide concrete moral judgment. The Good in the Right is a self-contained original contribution, but readers interested in ethics or its history will find numerous connections with classical and contemporary literature. Written with clarity and concreteness, and with examples for every major point, it provides an ethical theory that is both intellectually cogent and plausible in application to moral problems.
Elements Of Intuitionism
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Author : Michael Dummett
language : en
Publisher: Oxford University Press
Release Date : 2000
Elements Of Intuitionism written by Michael Dummett and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an informal but thorough introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics has been completely revised for this second edition. Brouwer's proof of the Bar Theorem has been reworked, the account of valuation systems simplified, and the treatment of generalized Beth Trees and the completeness of intuitionistic first-order logic rewritten. Readers are assumed to have some knowledge of classical formal logic and a general awareness of the history of intuitionism. From reviews of the first edition: This excellent book can be recommended to the student of mathematics or philosophy wishing to get a comprehensive and reliable introduction to modern intuitionism. Zentralblatt für Mathematik The relevance of this book extends well beyond the confines of the philosophy of mathematics, right to the centre of debates in the philosophy of language. Philosophical Books . . . a valuable and original contribution to the philosophy of mathematics. Journal of Symbolic Logic
Proof Theory
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Author : Katalin Bimbo
language : en
Publisher: CRC Press
Release Date : 2014-08-20
Proof Theory written by Katalin Bimbo and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-20 with Mathematics categories.
Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, linear logic, and modal logic. In the first chapters, the author emphasizes classical logic and a variety of different sequent calculi for classical and intuitionistic logics. She then presents other non-classical logics and meta-logical results, including decidability results obtained specifically using sequent calculus formalizations of logics. The book is suitable for a wide audience and can be used in advanced undergraduate or graduate courses. Computer scientists will discover intriguing connections between sequent calculi and resolution as well as between sequent calculi and typed systems. Those interested in the constructive approach will find formalizations of intuitionistic logic and two calculi for linear logic. Mathematicians and philosophers will welcome the treatment of a range of variations on calculi for classical logic. Philosophical logicians will be interested in the calculi for relevance logics while linguists will appreciate the detailed presentation of Lambek calculi and their extensions.