Mathematical Intuitionism Introduction To 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.
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.
An Introduction To Proof Theory
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Author : Paolo Mancosu
language : en
Publisher: Oxford University Press
Release Date : 2021
An Introduction To Proof Theory written by Paolo Mancosu 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 2021 with Mathematics categories.
"Proof theory is a central area of mathematical logic of special interest to philosophy . It has its roots in the foundational debate of the 1920s, in particular, in Hilbert's program in the philosophy of mathematics, which called for a formalization of mathematics, as well as for a proof, using philosophically unproblematic, "finitary" means, that these systems are free from contradiction. Structural proof theory investigates the structure and properties of proofs in different formal deductive systems, including axiomatic derivations, natural deduction, and the sequent calculus. Central results in structural proof theory are the normalization theorem for natural deduction, proved here for both intuitionistic and classical logic, and the cut-elimination theorem for the sequent calculus. In formal systems of number theory formulated in the sequent calculus, the induction rule plays a central role. It can be eliminated from proofs of sequents of a certain elementary form: every proof of an atomic sequent can be transformed into a "simple" proof. This is Hilbert's central idea for giving finitary consistency proofs. The proof requires a measure of proof complexity called an ordinal notation. The branch of proof theory dealing with mathematical systems such as arithmetic thus has come to be called ordinal proof theory. The theory of ordinal notations is developed here in purely combinatorial terms, and the consistency proof for arithmetic presented in detail"--
Basic Proof Theory
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Author : A. S. Troelstra
language : en
Publisher: Cambridge University Press
Release Date : 2000-07-27
Basic Proof Theory written by A. S. Troelstra 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 2000-07-27 with Computers categories.
This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.
Handbook Of Proof Theory
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Author : S.R. Buss
language : en
Publisher: Elsevier
Release Date : 1998-07-09
Handbook Of Proof Theory written by S.R. Buss and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-09 with Mathematics categories.
This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth.The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.
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
Automated Reasoning With Analytic Tableaux And Related Methods
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Author : Nicola Olivetti
language : en
Publisher: Springer
Release Date : 2007-09-17
Automated Reasoning With Analytic Tableaux And Related Methods written by Nicola Olivetti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-17 with Computers categories.
This book constitutes the refereed proceedings of the 16th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2007, held in Aix en Provence, France. It covers the wide range of logics, from intuitionistic and substructural logics to modal logics (including temporal and dynamic logics), from many-valued logics to nonmonotonic logics, and from classical first-order logic to description logics.
Proof Analysis
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Author : Sara Negri
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-29
Proof Analysis written by Sara Negri 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 2011-09-29 with Mathematics categories.
This book continues from where the authors' previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory and elementary geometry. The aim is, in each of the examples, to help the reader grasp the combinatorial behaviour of an axiom system, which typically leads to decidability results. The last part presents, as an application and extension of all that precedes it, a proof-theoretical approach to the Kripke semantics of modal and related logics, with a great number of new results, providing essential reading for mathematical and philosophical logicians.
Types For Proofs And Programs
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Author : Stefano Berardi
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-06-15
Types For Proofs And Programs written by Stefano Berardi 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 2004-06-15 with Computers categories.
This book constitutes the thoroughly refereed post-proceedings of the Third International Workshop of the Types Working Group, TYPES 2003, held in Torino, Italy in April/May 2003. The 25 revised full papers presented were carefully selected during two rounds of reviewing and improvement. All current issues in type theory and type systems and their applications to programming, systems design, and proof theory are addressed. Among the systems dealt with are Isabelle/Isar, PAF!, and Coq.
Classical And Nonclassical Logics
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Author : Eric Schechter
language : en
Publisher: Princeton University Press
Release Date : 2020-10-06
Classical And Nonclassical Logics written by Eric Schechter and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-06 with Mathematics categories.
So-called classical logic--the logic developed in the early twentieth century by Gottlob Frege, Bertrand Russell, and others--is computationally the simplest of the major logics, and it is adequate for the needs of most mathematicians. But it is just one of the many kinds of reasoning in everyday thought. Consequently, when presented by itself--as in most introductory texts on logic--it seems arbitrary and unnatural to students new to the subject. In Classical and Nonclassical Logics, Eric Schechter introduces classical logic alongside constructive, relevant, comparative, and other nonclassical logics. Such logics have been investigated for decades in research journals and advanced books, but this is the first textbook to make this subject accessible to beginners. While presenting an assortment of logics separately, it also conveys the deeper ideas (such as derivations and soundness) that apply to all logics. The book leads up to proofs of the Disjunction Property of constructive logic and completeness for several logics. The book begins with brief introductions to informal set theory and general topology, and avoids advanced algebra; thus it is self-contained and suitable for readers with little background in mathematics. It is intended primarily for undergraduate students with no previous experience of formal logic, but advanced students as well as researchers will also profit from this book.