A short introduction to intuitionistic logic:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Kluwer [u.a.]
2000
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| Series: | The university series in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 131 S. |
| ISBN: | 0306463946 |
Staff View
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Record in the Search Index
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| adam_text | A SHORT INTRODUCTION TO INTUITIONISTIC LOGIC GRIGORI MINTS STANFORD
UNIVERSITY STANFORD, CALIFORNIA KLUWER ACADEMIC /PLENUM PUBLISHERS NEW
YORK, BOSTON, DORDRECHT, LONDON, MOSCOW CONTENTS INTRODUCTION 1 I
INTUITIONISTIC PROPOSITIONAL LOGIC 5 1 PRELIMINARIES 7 2 NATURAL
DEDUCTION FOR PROPOSITIONAL LOGIC 9 2.1. SYNTAX 9 2.2. INTUITIONISTIC
PROPOSITIONAL SYSTEM NJP 10 2.3. CLASSICAL PROPOSITIONAL SYSTEM NKP 10
2.4. ABBREVIATED NOTATION FOR NATURAL DEDUCTIONS 11 2.5. DERIVABLE RULES
13 2.6. DIRECT CHAINING AND ANALYSIS INTO SUBGOALS 15 2.7. HEURISTICS
FOR NATURAL DEDUCTION 16 2.8. REPLACEMENT OF EQUIVALENTS 18 2.9.
CLASSICAL PROPOSITIONAL LOGIC 19 2.9.1. SEMANTICS: TRUTH TABLES 19
2.9.2. LOGICAL COMPUTATIONS 20 3 NEGATIVE TRANSLATION: GLIVENKO S
THEOREM 23 4 PROGRAM INTERPRETATION OF INTUITIONISTIC LOGIC 25 4.1.
BHK-INTERPRETATION 25 4.2. ASSIGNMENT T OF DEDUCTIVE TERMS 26 4.2.1.
ASSIGNMENT RULES 27 4.3. PROPERTIES OF TERM ASSIGNMENT T 29 5
COMPUTATIONS WITH DEDUCTIONS 31 5.1. CONVERSIONS AND REDUCTIONS OF
DEDUCTIVE TERMS 31 5.2. CONVERSIONS AND REDUCTIONS OF NATURAL DEDUCTIONS
32 5.3. NORMALIZATION 37 5.4. CONSEQUENCES OF NORMALIZATION 38 VII VUI
CONTENTS 6 COHERENCE THEOREM 41 6.1. STRUCTURE OF NORMAL DEDUCTION 41
6.2. ^-REDUCTION 42 6.3. COHERENCE THEOREM 42 7 KRIPKE MODELS 47 7.1.
SOUNDNESS OF THE SYSTEM NJP 50 7.2. POINTED FRAMES, PARTIAL ORDERS 51
7.3. FRAME CONDITIONS 52 8 GENTZEN-TYPE PROPOSITIONAL SYSTEM LJPM 53
8.1. SOUNDNESS OF THE SYSTEM LJPM 57 8.2. COMPLETENESS AND ADMISSIBILITY
OF CUT 57 8.3. TRANSLATION INTO THE PREDICATE LOGIC 61 8.4. ALGEBRAIC
MODELS 62 8.5. FILTRATION, FINITE MATRICES 65 8.5.1. FILTRATION 65
8.5.2. LINDENBAUM ALGEBRA 66 8.5.3. FINITE TRUTH TABLES 67 9 TOPOLOGICAL
COMPLETENESS 69 10 PROOF-SEARCH 75 10.1. TABLEAUX: SYSTEM LJPM* 75 10.2.
PROOF-SEARCH PROCEDURE 77 10.3. COMPLETE PROOF-SEARCH STRATEGY 79 11
SYSTEM LJP 83 11.1. TRANSLATING LJPM INTO LJP 83 11.2. A DISJUNCTIVE
TRANSLATION 83 11.3. PRUNING, PERMUTABILITY OF RULES 84 12 INTERPOLATION
THEOREM 89 12.1. BETH DEFINABILITY THEOREM 90 II INTUITIONISTIC
PREDICATE LOGIC 93 13 NATURAL DEDUCTION SYSTEM NJ 95 13.1. DERIVABLE
RULES 96 13.2. GODEL S NEGATIVE TRANSLATION 97 13.3. PROGRAM
INTERPRETATION OF NJ 99 14 KRIPKE MODELS FOR PREDICATE LOGIC 105 14.1.
POINTED MODELS, FRAME CONDITIONS 107 CONTENTS IX 15 SYSTEMS LJM, LJ 109
15.0.1. CANONICAL MODEL, ADMISSIBILITY OF CUT 109 15.1. TRANSLATION INTO
THE CLASSICAL LOGIC 113 15.2. SYSTEM LJ 114 15.2.1. TRANSLATING LJPM
INTO LJP 115 15.3. INTERPOLATION THEOREM 116 16 PROOF-SEARCH IN
PREDICATE LOGIC 119 REFERENCES 125 INDEX 129
|
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| indexdate | 2024-07-09T18:48:31Z |
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| isbn | 0306463946 |
| language | English |
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| physical | IX, 131 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| publisher | Kluwer [u.a.] |
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| series2 | The university series in mathematics |
| spelling | Mints, Grigorii E. Verfasser aut A short introduction to intuitionistic logic Grigori Mints New York [u.a.] Kluwer [u.a.] 2000 IX, 131 S. txt rdacontent n rdamedia nc rdacarrier The university series in mathematics Lambda-calcul ram Logique intuitionniste ram Mathématiques intuitionnistes démonstration théorème inriac logique intuitionniste inriac logique premier ordre inriac Intuitionistic mathematics Intuitionistische Logik (DE-588)4162199-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Intuitionistische Logik (DE-588)4162199-2 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009281795&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mints, Grigorii E. A short introduction to intuitionistic logic Lambda-calcul ram Logique intuitionniste ram Mathématiques intuitionnistes démonstration théorème inriac logique intuitionniste inriac logique premier ordre inriac Intuitionistic mathematics Intuitionistische Logik (DE-588)4162199-2 gnd |
| subject_GND | (DE-588)4162199-2 (DE-588)4151278-9 |
| title | A short introduction to intuitionistic logic |
| title_auth | A short introduction to intuitionistic logic |
| title_exact_search | A short introduction to intuitionistic logic |
| title_full | A short introduction to intuitionistic logic Grigori Mints |
| title_fullStr | A short introduction to intuitionistic logic Grigori Mints |
| title_full_unstemmed | A short introduction to intuitionistic logic Grigori Mints |
| title_short | A short introduction to intuitionistic logic |
| title_sort | a short introduction to intuitionistic logic |
| topic | Lambda-calcul ram Logique intuitionniste ram Mathématiques intuitionnistes démonstration théorème inriac logique intuitionniste inriac logique premier ordre inriac Intuitionistic mathematics Intuitionistische Logik (DE-588)4162199-2 gnd |
| topic_facet | Lambda-calcul Logique intuitionniste Mathématiques intuitionnistes démonstration théorème logique intuitionniste logique premier ordre Intuitionistic mathematics Intuitionistische Logik Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009281795&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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