Natural Deduction
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Natural Deduction
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Author : Dag Prawitz
language : en
Publisher: Courier Dover Publications
Release Date : 2006-02-24
Natural Deduction written by Dag Prawitz and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-24 with Mathematics categories.
An innovative approach to the semantics of logic, proof-theoretic semantics seeks the meaning of propositions and logical connectives within a system of inference. Gerhard Gentzen invented proof-theoretic semantics in the early 1930s, and Dag Prawitz, the author of this study, extended its analytic proofs to systems of natural deduction. Prawitz's theories form the basis of intuitionistic type theory, and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics. The concept of natural deduction follows a truly natural progression, establishing the relationship between a noteworthy systematization and the interpretation of logical signs. As this survey explains, the deduction's principles allow it to proceed in a direct fashion — a manner that permits every natural deduction's transformation into the equivalent of normal form theorem. A basic result in proof theory, the normal form theorem was established by Gentzen for the calculi of sequents. The proof of this result for systems of natural deduction is in many ways simpler and more illuminating than alternative methods. This study offers clear illustrations of the proof and numerous examples of its advantages.
Natural Deduction
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Author : John Mueller Anderson
language : en
Publisher:
Release Date : 1962
Natural Deduction written by John Mueller Anderson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Logic, Symbolic and mathematical categories.
Natural Deduction
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Author : Richard Thomas William Arthur
language : en
Publisher:
Release Date : 2011
Natural Deduction written by Richard Thomas William Arthur and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Logic categories.
Natural Deduction
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Author : Richard T.W. Arthur
language : en
Publisher: Broadview Press
Release Date : 2011-05-25
Natural Deduction written by Richard T.W. Arthur and has been published by Broadview Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-25 with Philosophy categories.
Richard Arthur’s Natural Deduction provides a wide-ranging introduction to logic. In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python.
Advances In Natural Deduction
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Author : Luiz Carlos Pereira
language : en
Publisher: Springer
Release Date : 2014-07-08
Advances In Natural Deduction written by Luiz Carlos Pereira and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-08 with Philosophy categories.
This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz’s work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics and Theoretical Computer Science. The range of contributions includes material on the extension of natural deduction with higher-order rules, as opposed to higher-order connectives, and a paper discussing the application of natural deduction rules to dealing with equality in predicate calculus. The volume continues with a key chapter summarizing work on the extension of the Curry-Howard isomorphism (itself a by-product of the work on natural deduction), via methods of category theory that have been successfully applied to linear logic, as well as many other contributions from highly regarded authorities. With an illustrious group of contributors addressing a wealth of topics and applications, this volume is a valuable addition to the libraries of academics in the multiple disciplines whose development has been given added scope by the methodologies supplied by natural deduction. The volume is representative of the rich and varied directions that Prawitz work has inspired in the area of natural deduction.
Natural Deduction
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Author : John Mueller Anderson
language : en
Publisher:
Release Date : 2013-03
Natural Deduction written by John Mueller Anderson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03 with Literary Collections categories.
""Natural Deduction: The Logical Basis Of Axiom Systems"" by Anderson and Mueller is a comprehensive introduction to the natural deduction method of proof in logic. The book presents a clear and concise explanation of the principles of natural deduction, including the use of assumptions, conditional proofs, and indirect proofs. The authors also provide a thorough overview of the different types of axioms and the role they play in logical systems. The book is organized into six chapters, each of which covers a different aspect of natural deduction. Chapter one introduces the basic concepts of logic and sets the stage for the rest of the book. Chapter two provides an in-depth explanation of the natural deduction method, including the rules of inference and the use of truth tables. Chapter three focuses on the use of assumptions in natural deduction, while chapter four covers the use of conditional proofs. Chapter five explores the use of indirect proofs, including proof by contradiction and proof by contrapositive. Finally, chapter six provides an overview of axiom systems and the different types of axioms that are commonly used in logic. Throughout the book, the authors provide numerous examples and exercises to help readers develop their understanding of natural deduction and axiom systems. Overall, ""Natural Deduction: The Logical Basis Of Axiom Systems"" is an excellent resource for anyone interested in learning about logic and proof theory. The book is written in a clear and accessible style, making it suitable for both beginners and more advanced readers. Whether you are a student of philosophy, mathematics, or computer science, this book is sure to provide valuable insights into the principles of natural deduction and the logical basis of axiom systems.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.
An Introduction To Logic Second Edition
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Author : Richard T.W. Arthur
language : en
Publisher: Broadview Press
Release Date : 2016-11-30
An Introduction To Logic Second Edition written by Richard T.W. Arthur and has been published by Broadview Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-30 with Philosophy categories.
In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python. A previous edition of this book appeared under the title Natural Deduction. This new edition adds clarifications of the notions of explanation, validity and formal validity, a more detailed discussion of derivation strategies, and another rule of inference, Reiteration.
Natural Deduction Hybrid Systems And Modal Logics
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Author : Andrzej Indrzejczak
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-03
Natural Deduction Hybrid Systems And Modal Logics written by Andrzej Indrzejczak 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 2010-07-03 with Philosophy categories.
A good title should be informative enough to illuminate a potential reader on the content of a book. We hope that the present title gives at least some hints of what this book is about. The notion of natural deduction or modal logic are rather well known, but the notion of “hybrid system” certainly needs some explanation. In short, this study may be seen as a kind of search for good deductive systems. We think of systems good in practice which may be applied with easenotonlybywelltrainedlogiciansbutalso, forexample, byphilosophers who need handy deductive tools accompanying their analyses. In parti- lar, we are interested in providing systems that may be widely applied in teaching logic. Nowadays one may observe that several courses in “critical thinking” tend to eliminate courses in practical logic. On the other hand, logic is often taught as a strictly mathematical discipline in very dema- ing courses. It is important to ?ll the gap between these extrema, and the crucial ingredient of any course which is supposed to teach how to use logic, is certainly a suitable deductive system. Since we address this work to a wide audience interested in applications of logic, we were trying to make it self-contained and accessible to a reader with no hard training in logic. The assumed reader should have some ba- ground in logic (an elementary course covering classical propositional and ?rst-order logic with basics of set theory is enough) but not necessarily in modal logic.
Natural Deduction The Logical Basis Of Axiom Systems
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Author : John Mueller Anderson
language : en
Publisher:
Release Date : 1952
Natural Deduction The Logical Basis Of Axiom Systems written by John Mueller Anderson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1952 with Logic, Symbolic and mathematical categories.
Natural Deduction
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Author : John Mueller Anderson
language : en
Publisher:
Release Date : 1962
Natural Deduction written by John Mueller Anderson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Model theory categories.