Automated deduction in multiple-valued logics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Oxford u.a.
Clarendon Press
1993
|
| Series: | The international series of monographs on computer science
10 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 172 S. graph. Darst. |
| ISBN: | 0198539894 |
Staff View
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| 245 | 1 | 0 | |a Automated deduction in multiple-valued logics |c Reiner Hähnle |
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Record in the Search Index
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| adam_text | AUTOMATED DEDUCTION IN MULTIPLE-VALUED LOGICS REINER HAEHNLE UNIVERSITY
OF KARLSRUHE CLARENDON PRESS OXFORD 1993 CONTENTS 1 INTRODUCTION 1 2
PRELIMINARIES 4 2.1 ABSTRACT ALGEBRAS 4 2.2 SYNTAX AND SEMANTICS 5 2.3
EXAMPLES OF MULTIPLE-VALUED LOGICS 11 2.3.1 THE LOGICS OF KLEENE AND OF
ROSSER AND TUR- QUETTE 12 2.3.2 LUKASIEWICZ LOGICS 13 2.3.3 POST LOGICS
14 3 THE LOGICAL BASIS: SIGNED ANALYTIC TABLEAUX 15 INTRODUCTION TO
CHAPTERS 3 TO 6 15 3.1 SIGNED TABLEAUX FOR CLASSICAL LOGIC 16 3.2 ON THE
ROELE OF SIGNS IN ANALYTIC TABLEAUX 22 3.3 MULTIPLE-VALUED EXTENSION OF
TABLEAU SYSTEMS 23 3.4 DISCUSSION 29 4 A NEW TECHNIQUE: TRUTH VALUE SETS
AS SIGNS 32 4.1 SETS AS SIGNS 32 4.2 SOUNDNESS 40 4.3 COMPLETENESS 42
4.4 SIZE OF PROOF TREES 47 4.5 FUNCTION MINIMIZATION 50 5 UNIFORM
NOTATION REGAINED: REGULAER LOGICS 55 5.1 PRIMARY MULTIPLE-VALUED
CONNECTIVES 55 5.2 REGULAER LOGICS 59 5.3 ON THE SCOPE OF REGULAER LOGICS
68 5.4 FIRST-ORDER MULTIPLE-VALUED LOGICS 71 5.5 EXTENSIONS 77 VLLL
CONTENTS 6 BEYOND TABLEAUX 81 6.1 LEMMA GENERATION*ASYMMETRIC
RULES*ANALYTIC CUT 81 6.1.1 LEMMA GENERATION AND ASYMMETRIC RULES 81
6.1.2 KE SYSTEMS AND THE PRINCIPLE OF BIVALENCE 83 6.1.3 LEMMA
GENERATION IN MULTIPLE-VALUED LOGICS 85 6.1.4 THE PRINCIPLE OF
MULTIVALENCE 87 6.2 TABLEAUX AS INTEGER PROGRAMMING PROBLEMS 89 6.2.1
MIXED INTEGER PROGRAMMING 89 6.2.2 TABLEAU PROOFS WITH CONSTRAINTS 91
6.2.3 EXAMPLE 94 6.2.4 COMPLEXITY OF MULTIPLE-VALUED LOGICS 95 6.2.5 A
REDUCTION FROM MULTIPLE-VALUED DEDUCTION TO BMIP 96 6.2.5.1 NEGATION 98
6.2.6 MIP FORMULATION OF C U 99 6.2.7 OUTLOOK 101 6.3 OTHER INFERENCE
SYSTEMS 102 6.3.1 TECHNIQUES COMMON TO TABLEAU-LIKE CALCULI 102 6.3.1.1
PROOF REPRESENTATION 102 6.3.1.2 FREE VARIABLES 102 6.3.2 DECISION
DIAGRAMS 103 6.3.3 EXTENDING MULTIPLE-VALUED DISSOLUTION 104 6.3.4
RESOLUTION 105 6.4 EVALUATION 107 6.4.1 EVALUATING THE CRITERIA FROM THE
INTRODUCTION 107 6.4.2 SOME EXPERIMENTAL RESULTS 108 6.4.3 OUTLOOK 109 7
APPLICATIONS 110 7.1 OVERVIEW 110 7.2 APPLICATIONS OF A THEORETICAL
NATURE 112 7.2.1 INDEPENDENCE PROOFS IN HUBERT SYSTEMS 112 7.2.2
RELEVANCE LOGIC: A SPECIAL CASE 113 7.2.3 SUCHOII S TABLEAU SYSTEM:
ANOTHER SPECIAL CASE 115 7.2.4 IMPROVEMENT OF AN S5-IMPLEMENTATION BY
CA- FERRA AND ZABEL 116 7.3 APPLICATIONS OF A PRACTICA! NATURE 117 7.3.1
INTERVAL ARITHMETIC 117 7.3.2 HARDWARE VERIFICATION 117 CONTENTS IX 8 A
HISTORY OF MULTIPLE-VALUED THEOREM PROV- ING 120 INTRODUCTION 120 8.1
RESOLUTION-BASED SYSTEMS 121 8.1.1 MORGAN S RESOLUTION-BASED SYSTEM 121
8.1.2 SCHMITT S RESOLUTION-BASED SYSTEM 125 8.1.3 STACHNIAK S RESOLUTION
LOGICS 127 8.1.4 RESOLUTION-BASED SYSTEMS FOR FUZZY LOGIC 133 8.1.4.1
LEE AND CHANG S RESOLUTION-BASED SY- STEM 134 8.1.4.2 EXTENDED POST
LOGICS 134 8.1.4.3 U + L-VALUED POST LOGICS 136 8.1.5 PARACONSISTENT
LOGICS 138 8.2 OTHER APPROACHES 139 8.2.1 DECISION DIAGRAMS 139 8.2.1.1
BINARY DECISION DIAGRAMS 139 8.2.1.2 N-ARY DECISION DIAGRAMS 140 8.2.1.3
MULTIPLE-VALUED DEDUCTION AS A UNI- FICATION PROBLEM 142 8.2.2
APPROACHES BASED ON TABLEAUX AND GENTZEN CALCULI 143 8.2.3 PATH
DISSOLUTION BY MURRAY AND ROSENTHAL 144 8.2.4 BEAVERS APPROACH TO
LUKASIEWICZ LOGIC 147 8.2.5 MELLOULI S THREE-VALUED EXTENSION OF
PLAISTED S MODIFIED PROBLEM REDUCTION FORMAT 148 8.2.6 GENERAL
FRAMEWORKS 151 8.2.6.1 AUTOLOGIC 151 8.2.6.2 LABELLED DEDUCTIVE SYSTEMS
151 8.3 DISCUSSION 152 9 CONCLUSION 154 REFERENCES 156 INDEX 169
|
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| isbn | 0198539894 |
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| spelling | Hähnle, Reiner Verfasser (DE-588)136037542 aut Automated deduction in multiple-valued logics Reiner Hähnle Oxford u.a. Clarendon Press 1993 IX, 172 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The international series of monographs on computer science 10 Teilw. zugl.: Karlsruhe, Univ., Diss., 1991 Logique symbolique et mathématique Logique symbolique et mathématique ram Théorèmes - Démonstration automatique Théorèmes - Démonstration automatique ram déduction automatique inriac démonstration théorème inriac logique plurivalente inriac Automatic theorem proving Logic, Symbolic and mathematical Mehrwertige Logik (DE-588)4169335-8 gnd rswk-swf Temporale Logik (DE-588)4137542-7 gnd rswk-swf Automatisches Beweisverfahren (DE-588)4069034-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Temporale Logik (DE-588)4137542-7 s Automatisches Beweisverfahren (DE-588)4069034-9 s DE-604 Mehrwertige Logik (DE-588)4169335-8 s DE-188 The international series of monographs on computer science 10 (DE-604)BV000725123 10 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006393339&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hähnle, Reiner Automated deduction in multiple-valued logics The international series of monographs on computer science Logique symbolique et mathématique Logique symbolique et mathématique ram Théorèmes - Démonstration automatique Théorèmes - Démonstration automatique ram déduction automatique inriac démonstration théorème inriac logique plurivalente inriac Automatic theorem proving Logic, Symbolic and mathematical Mehrwertige Logik (DE-588)4169335-8 gnd Temporale Logik (DE-588)4137542-7 gnd Automatisches Beweisverfahren (DE-588)4069034-9 gnd |
| subject_GND | (DE-588)4169335-8 (DE-588)4137542-7 (DE-588)4069034-9 (DE-588)4113937-9 |
| title | Automated deduction in multiple-valued logics |
| title_auth | Automated deduction in multiple-valued logics |
| title_exact_search | Automated deduction in multiple-valued logics |
| title_full | Automated deduction in multiple-valued logics Reiner Hähnle |
| title_fullStr | Automated deduction in multiple-valued logics Reiner Hähnle |
| title_full_unstemmed | Automated deduction in multiple-valued logics Reiner Hähnle |
| title_short | Automated deduction in multiple-valued logics |
| title_sort | automated deduction in multiple valued logics |
| topic | Logique symbolique et mathématique Logique symbolique et mathématique ram Théorèmes - Démonstration automatique Théorèmes - Démonstration automatique ram déduction automatique inriac démonstration théorème inriac logique plurivalente inriac Automatic theorem proving Logic, Symbolic and mathematical Mehrwertige Logik (DE-588)4169335-8 gnd Temporale Logik (DE-588)4137542-7 gnd Automatisches Beweisverfahren (DE-588)4069034-9 gnd |
| topic_facet | Logique symbolique et mathématique Théorèmes - Démonstration automatique déduction automatique démonstration théorème logique plurivalente Automatic theorem proving Logic, Symbolic and mathematical Mehrwertige Logik Temporale Logik Automatisches Beweisverfahren Hochschulschrift |
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