Holdings: Structural proof theory

Structural proof theory:

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Bibliographic Details
Main Authors:	Negri, Sara 1967- (Author), Plato, Jan von 1951- (Author)
Format:	Book
Language:	English
Published:	Cambridge [u.a.] Cambridge Univ. Press 2001
Edition:	1. publ.
Subjects:	Beweistheorie
Online Access:	Inhaltsverzeichnis
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	XVII, 257 S.
ISBN:	0521793076 9780521793070 9780521068420

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MARC


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adam_text	IMAGE 1 STRUCTURAL PROOF THEORY SARA NEGRI JAN VON PLATO WITH AN APPENDIX BY AAME RANTA CAMBRIDGE UNIVERSITY PRESS IMAGE 2 CONTENTS PREFACE PAGE IX INTRODUCTION XI STRUCTURAL PROOF THEORY XI USE OF THIS BOOK IN TEACHING XIV WHAT IS NEW IN THIS BOOK? XVI 1. FROM NATURAL DEDUCTION TO SEQUENT CALCULUS 1 1.1. LOGICAL SYSTEMS 1 1.2. NATURAL DEDUCTION 5 1.3. FROM NATURAL DEDUCTION TO SEQUENT CALCULUS 13 1.4. THE STRUCTURE OF PROOFS 20 NOTES TO CHAPTER 1 23 2. SEQUENT CALCULUS FOR INTUITIONISTIC LOGIC 25 2.1. CONSTRUCTIVE REASONING 25 2.2. INTUITIONISTIC SEQUENT CALCULUS 28 2.3. PROOF METHODS FOR ADMISSIBILITY 30 2.4. ADMISSIBILITY OF CONTRACTION AND CUT 33 2.5. SOME CONSEQUENCES OF CUT ELIMINATION 40 NOTES TO CHAPTER 2 46 3. SEQUENT CALCULUS FOR CLASSICAL LOGIC 47 3.1. AN INVERTIBLE CLASSICAL CALCULUS 48 3.2. ADMISSIBILITY OF STRUCTURAL RULES 53 3.3. COMPLETENESS 58 NOTES TO CHAPTER 3 60 4. THE QUANTIFIERS 61 4.1. QUANTIFIERS IN NATURAL DEDUCTION AND IN SEQUENT CALCULUS 61 4.2. ADMISSIBILITY OF STRUCTURAL RULES 70 IMAGE 3 VI CONTENTS 4.3. APPLICATIONS OF CUT ELIMINATION 76 4.4. COMPLETENESS OF CLASSICAL PREDICATE LOGIC 81 NOTES TO CHAPTER 4 86 5. VARIANTS OF SEQUENT CALCULI 87 5.1. SEQUENT CALCULI WITH INDEPENDENT CONTEXTS 87 5.2. SEQUENT CALCULI IN NATURAL DEDUCTION STYLE 98 5.3. AN INTUITIONISTIC MULTISUCCEDENT CALCULUS 108 5.4. A CLASSICAL SINGLE SUCCEDENT CALCULUS 114 5.5. A TERMINATING INTUITIONISTIC CALCULUS 122 NOTES TO CHAPTER 5 124 6. STRUCTURAL PROOF ANALYSIS OF AXIOMATIC THEORIES 126 6.1. FROM AXIOMS TO RULES 126 6.2. ADMISSIBILITY OF STRUCTURAL RULES 131 6.3. FOUR APPROACHES TO EXTENSION BY AXIOMS 134 6.4. PROPERTIES OF CUT-FREE DERIVATIONS 136 6.5. PREDICATE LOGIC WITH EQUALITY 138 6.6. APPLICATION TO AXIOMATIC SYSTEMS 141 NOTES TO CHAPTER 6 154 7. INTERMEDIATE LOGICAL SYSTEMS 156 7.1. A SEQUENT CALCULUS FOR THE WEAK LAW OF EXCLUDED MIDDLE 157 7.2. A SEQUENT CALCULUS FOR STABLE LOGIC 158 7.3. SEQUENT CALCULI FOR DUMMETT LOGIC 160 NOTES TO CHAPTER 7 164 8. BACK TO NATURAL DEDUCTION 165 8.1. NATURAL DEDUCTION WITH GENERAL ELIMINATION RULES 166 8.2; TRANSLATION FROM SEQUENT CALCULUS TO NATURAL DEDUCTION 172 8.3. TRANSLATION FROM NATURAL DEDUCTION TO SEQUENT CALCULUS 179 8.4. DERIVATIONS WITH CUTS AND NON-NORMAL DERIVATIONS 185 8.5. THE STRUCTURE OF NORMAL DERIVATIONS 189 8.6. CLASSICAL NATURAL DEDUCTION FOR PROPOSITIONAL LOGIC 202 NOTES TO CHAPTER 8 208 CONCLUSION: DIVERSITY AND UNITY IN STRUCTURAL PROOF THEORY 211 COMPARING SEQUENT CALCULUS AND NATURAL DEDUCTION 211 A UNIFORM LOGICAL CALCULUS 213 APPENDIX A: SIMPLE TYPE THEORY AND CATEGORIAL GRAMMAR 219 A. 1. SIMPLE TYPE THEORY 219 A.2. CATEGORIAL GRAMMAR FOR LOGICAL LANGUAGES 221 NOTES TO APPENDIX A 224 IMAGE 4 CONTENTS VII APPENDIX B: PROOF THEORY AND CONSTRUCTIVE TYPE THEORY 225 B.I. LOWER-LEVEL TYPE THEORY 225 B.2. HIGHER-LEVEL TYPE THEORY 230 B.3. TYPE SYSTEMS 232 NOTES TO APPENDIX B 234 APPENDIX C: PESCA - A PROOF EDITOR FOR SEQUENT CALCULUS 235 (BY AARNE RANTA) C.I. INTRODUCTION 235 C.2. TWO EXAMPLE SESSIONS 236 C.3. SOME COMMANDS 239 C.4. AXIOM FILES 241 C.5. ON THE IMPLEMENTATION 242 NOTES TO APPENDIX C 243 ELECTRONIC REFERENCES 243 BIBLIOGRAPHY 245 AUTHOR INDEX 251 SUBJECT INDEX 253 INDEX OF LOGICAL SYSTEMS 257
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author	Negri, Sara 1967- Plato, Jan von 1951-
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discipline	Mathematik Philosophie
edition	1. publ.
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spelling	Negri, Sara 1967- Verfasser (DE-588)173487084 aut Structural proof theory Sara Negri ; Jan von Plato 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2001 XVII, 257 S. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Beweistheorie (DE-588)4145177-6 gnd rswk-swf Beweistheorie (DE-588)4145177-6 s DE-604 Plato, Jan von 1951- Verfasser (DE-588)171423615 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009516859&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Negri, Sara 1967- Plato, Jan von 1951- Structural proof theory Beweistheorie (DE-588)4145177-6 gnd
subject_GND	(DE-588)4145177-6
title	Structural proof theory
title_auth	Structural proof theory
title_exact_search	Structural proof theory
title_full	Structural proof theory Sara Negri ; Jan von Plato
title_fullStr	Structural proof theory Sara Negri ; Jan von Plato
title_full_unstemmed	Structural proof theory Sara Negri ; Jan von Plato
title_short	Structural proof theory
title_sort	structural proof theory
topic	Beweistheorie (DE-588)4145177-6 gnd
topic_facet	Beweistheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009516859&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT negrisara structuralprooftheory AT platojanvon structuralprooftheory

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