Combinators Terms And Proof Theory
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Combinators Terms And Proof Theory
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Author : S. Stenlund
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Combinators Terms And Proof Theory written by S. Stenlund 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.
The aim of this monograph is to present some of the basic ideas and results in pure combinatory logic and their applications to some topics in proof theory, and also to present some work of my own. Some of the material in chapter 1 and 3 has already appeared in my notes Introduction to Combinatory Logic. It appears here in revised form since the presen tation in my notes is inaccurate in several respects. I would like to express my gratitude to Stig Kanger for his invalu able advice and encouragement and also for his assistance in a wide variety of matters concerned with my study in Uppsala. I am also in debted to Per Martin-USf for many valuable and instructive conversa tions. As will be seen in chapter 4 and 5, I also owe much to the work of Dag Prawitz and W. W. Tait. My thanks also to Craig McKay who read the manuscript and made valuable suggestions. I want, however, to emphasize that the shortcomings that no doubt can be found, are my sole responsibility. Uppsala, February 1972.
Combinators Lambda Terms And Proof Theory
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Author : S. Stenlund
language : en
Publisher: Springer
Release Date : 1972-09-30
Combinators Lambda Terms And Proof Theory written by S. Stenlund and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-09-30 with Philosophy categories.
Logical Theory And Semantic Analysis
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Author : Stig Kanger
language : en
Publisher: Springer Science & Business Media
Release Date : 1974-06-30
Logical Theory And Semantic Analysis written by Stig Kanger 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 1974-06-30 with Philosophy categories.
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.
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
Recursive Algebra Analysis And Combinatorics
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Author :
language : en
Publisher: Elsevier
Release Date : 1998-11-30
Recursive Algebra Analysis And Combinatorics written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-30 with Computers categories.
Recursive Algebra, Analysis and Combinatorics
Metamathematical Investigation Of Intuitionistic Arithmetic And Analysis
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Author : Anne S. Troelstra
language : en
Publisher: Springer
Release Date : 2006-11-15
Metamathematical Investigation Of Intuitionistic Arithmetic And Analysis 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 2006-11-15 with Mathematics categories.
Combinatorics On Words
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Author : M. Lothaire
language : en
Publisher: Cambridge University Press
Release Date : 1997-05-29
Combinatorics On Words written by M. Lothaire 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 1997-05-29 with Mathematics categories.
Combinatorics on words, or finite sequences, is a field which grew simultaneously within disparate branches of mathematics such as group theory and probability. It has grown into an independent theory finding substantial applications in computer science automata theory and liguistics. This volume is the first to present a thorough treatment of this theory. All of the main results and techniques are covered. The presentation is accessible to undergraduate and graduate level students in mathematics and computer science as well as to specialists in all branches of applied mathematics.
Action Theory
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Author : M. Brand
language : en
Publisher: Springer Science & Business Media
Release Date : 1976-09-30
Action Theory written by M. Brand 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 1976-09-30 with Philosophy categories.
Proceedings of the Winnipeg Conference on Human Action, held at Winnipeg, Manitoba, Canada, 9-11 May 1975
Algebraic Combinatorics On Words
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Author : M. Lothaire
language : en
Publisher: Cambridge University Press
Release Date : 2002-04-18
Algebraic Combinatorics On Words written by M. Lothaire 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 2002-04-18 with Mathematics categories.
Comprehensive 2002 introduction to combinatorics on words for mathematicians and theoretical computer scientists.