The Functional Interpretation Of Logical Deduction
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The Functional Interpretation Of Logical Deduction
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Author : Ruy J. G. B. de Queiroz
language : en
Publisher: World Scientific
Release Date : 2012
The Functional Interpretation Of Logical Deduction written by Ruy J. G. B. de Queiroz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Computers categories.
This comprehensive book provides an adequate framework to establish various calculi of logical inference. Being an ?enriched? system of natural deduction, it helps to formulate logical calculi in an operational manner. By uncovering a certain harmony between a functional calculus on the labels and a logical calculus on the formulas, it allows mathematical foundations for systems of logic presentation designed to handle meta-level features at the object-level via a labelling mechanism, such as the D Gabbay's Labelled Deductive Systems. The book truly demonstrates that introducing ?labels? is useful to understand the proof-calculus itself, and also to clarify its connections with model-theoretic interpretations.
The Functional Interpretation Of Logical Deduction
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Author : Anjolina G. de Oliveira
language : en
Publisher: World Scientific
Release Date : 2012
The Functional Interpretation Of Logical Deduction written by Anjolina G. de Oliveira and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Computers categories.
This comprehensive book provides an adequate framework to establish various calculi of logical inference. Being an OCyenrichedOCO system of natural deduction, it helps to formulate logical calculi in an operational manner. By uncovering a certain harmony between a functional calculus on the labels and a logical calculus on the formulas, it allows mathematical foundations for systems of logic presentation designed to handle meta-level features at the object-level via a labelling mechanism, such as the D Gabbay's Labelled Deductive Systems. The book truly demonstrates that introducing OCylabelsOCO is useful to understand the proof-calculus itself, and also to clarify its connections with model-theoretic interpretations.
Logic Language And Reasoning
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Author : Hans Jürgen Ohlbach
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Logic Language And Reasoning written by Hans Jürgen Ohlbach 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 Philosophy categories.
th This volume is dedicated to Dov Gabbay who celebrated his 50 birthday in October 1995. Dov is one of the most outstanding and most productive researchers we have ever met. He has exerted a profound influence in major fields of logic, linguistics and computer science. His contributions in the areas of logic, language and reasoning are so numerous that a comprehensive survey would already fill half of this book. Instead of summarizing his work we decided to let him speak for himself. Sitting in a car on the way to Amsterdam airport he gave an interview to Jelle Gerbrandy and Anne-Marie Mineur. This recorded conversation with him, which is included gives a deep insight into his motivations and into his view of the world, the Almighty and, of course, the role of logic. In addition, this volume contains a partially annotated bibliography of his main papers and books. The length of the bibliography and the broadness of the topics covered there speaks for itself.
Logic Form And Function
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Author : John Alan Robinson
language : en
Publisher: North Holland
Release Date : 1979
Logic Form And Function written by John Alan Robinson and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Philosophy categories.
Logic: form and content; Formulas: syntax and intuitive semantics; Boolean analysis of sentences; Infinitive finitary trees and boolean compactness; Semantic analysis of sentences and terms; Logical consequence: sequents and proofs; Logical equivalence: substitutivity and variants; Normal forms of sentences and sequents; Herbrand models and maps; Quad notation for clausal sequents; Unification; Resolution; Resolution on the computer; Historical notes; Appedix; Index.
Well Quasi Orders In Computation Logic Language And Reasoning
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Author : Peter M. Schuster
language : en
Publisher: Springer Nature
Release Date : 2020-01-01
Well Quasi Orders In Computation Logic Language And Reasoning written by Peter M. Schuster and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-01 with Philosophy categories.
This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students.
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.
Proof Theory And Automated Deduction
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Author : Jean Goubault-Larrecq
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-30
Proof Theory And Automated Deduction written by Jean Goubault-Larrecq 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 2001-11-30 with Computers categories.
Interest in computer applications has led to a new attitude to applied logic in which researchers tailor a logic in the same way they define a computer language. In response to this attitude, this text for undergraduate and graduate students discusses major algorithmic methodologies, and tableaux and resolution methods. The authors focus on first-order logic, the use of proof theory, and the computer application of automated searches for proofs of mathematical propositions. Annotation copyrighted by Book News, Inc., Portland, OR
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.
Deductive Logic
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Author : Warren Goldfarb
language : en
Publisher: Hackett Publishing
Release Date : 2003-09-15
Deductive Logic written by Warren Goldfarb and has been published by Hackett Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-15 with Philosophy categories.
This text provides a straightforward, lively but rigorous, introduction to truth-functional and predicate logic, complete with lucid examples and incisive exercises, for which Warren Goldfarb is renowned.
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.