An introduction to many-valued and fuzzy logic: semantics, algebras, and derivation systems
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2008
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Table of contents only Contributor biographical information Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 321-325) and index |
| Physical Description: | xii, 329 p. ill. |
| ISBN: | 0521881285 9780521881289 0521707579 9780521707572 |
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MARC
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| 245 | 1 | 0 | |a An introduction to many-valued and fuzzy logic |b semantics, algebras, and derivation systems |c Merrie Bergmann |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2008 | |
| 300 | |a xii, 329 p. |b ill. | ||
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| 500 | |a Includes bibliographical references (p. 321-325) and index | ||
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| adam_text | AN INTRODUCTION TO MANY-VALUED AND FUZZY LOGIC SEMANTICS, ALGEBRAS, AND
DEBIATION SYSTEMS MERRIE BERGMANN EMERITA, SMITH COLLEGE CAMBRIDGE
UNIVERSITY PRESS CONTENTS PREFACE PAGE XI 1 INTRODUCTION 1.1 ISSUES OF
VAGUENESS 1 1.2 VAGUENESS DENNED 5 1.3 THE PROBLEM OF THE FRINGE 6 1.4
PREVIEW OF THE REST OF THE BOOK 7 1.5 HISTORY AND SCOPE OF FUZZY LOGIC 8
1.6 TALL PEOPLE 10 1.7 EXERCISES 10 2 REVIEW OF CLASSICAL PREPOSITIONAL
LOGIC 12 2.1 THE LANGUAGE OF CLASSICAL PROPOSITIONAL LOGIC 12 2.2
SEMANTICS OF CLASSICAL PROPOSITIONAL LOGIC 13 2.3 NORMAL FORMS 18 2.4 AN
AXIOMATIC DERIVATION SYSTEM FOR CLASSICAL PROPOSITIONAL LOGIC 21 2.5
FUNCTIONAL COMPLETENESS 32 2.6 DECIDABILITY 35 2.7 EXERCISES 36 3 REVIEW
OF CLASSICAL FIRST-ORDER LOGIC 39 3.1 THE LANGUAGE OF CLASSICAL
FIRST-ORDER LOGIC 39 3.2 SEMANTICS OF CLASSICAL FIRST-ORDER LOGIC 42 3.3
AN AXIOMATIC DERIVATION SYSTEM FOR CLASSICAL FIRST-ORDER LOGIC 49 3.4
EXERCISES 55 4 ALTERNATIVE SEMANTICS FOR TRUTH-VALUES AND
TRUTH-FUNCTIONS: NUMERIC TRUTH-VALUES AND ABSTRACT ALGEBRAS 57 4.1
NUMERIC TRUTH-VALUES FOR CLASSICAL LOGIC 57 4.2 BOOLEAN ALGEBRAS AND
CLASSICAL LOGIC 59 4.3 MORE RESULTS ABOUT BOOLEAN ALGEBRAS 63 ** * 4.4
EXERCISES 69 VIII CONTENTS 5 THREE-VALUED PROPOSITIONAL LOGICS:
SEMANTICS 71 5.1 KLEENE S STRONG THREE-VALUED LOGIC . 71 5.2
LUKASIEWICZ S THREE-VALUED LOGIC 76 5.3 BOCHVAR S THREE-VALUED LOGICS 80
5.4 EVALUATING THREE-VALUED SYSTEMS; QUASI-TAUTOLOGIES AND
QUASI-CONTRADICTIONS 84 5.5 NORMAL FORMS 89 5.6 QUESTIONS OF
INTERDEFINABILITY BETWEEN THE SYSTEMS AND FUNCTIONAL COMPLETENESS 90 5.7
LUKASIEWICZ S SYSTEM EXPANDED 94 5.8 EXERCISES 96 6 DERIVATION SYSTEMS
FOR THREE-VALUED PROPOSITIONAL LOGIC 100 6.1 AN AXIOMATIC SYSTEM FOR
TAUTOLOGIES AND VALIDITY IN THREE-VALUED LOGIC 100 6.2 A PAVELKA-STYLE
DERIVATION SYSTEM FOR L 3 114 6.3 EXERCISES 126 7 THREE-VALUED
FIRST-ORDER LOGICS: SEMANTICS 130 7.1 A FIRST-ORDER GENERALIZATION OF L
3 130 7.2 QUANTIFIERS BASED ON THE OTHER THREE-VALUED SYSTEMS 137 7.3
TAUTOLOGIES, VALIDITY, AND QUASI- SEMANTIC CONCEPTS 140 7.4 EXERCISES
143 8 DERIVATION SYSTEMS FOR THREE-VALUED FIRST-ORDER LOGIC 146 8.1 AN
AXIOMATIC SYSTEM FOR TAUTOLOGIES AND VALIDITY IN THREE-VALUED
FIRST-ORDER LOGIC 146 8.2 A PAVELKA-STYLE DERIVATION SYSTEM FOR L 3 V
153 8.3 EXERCISES 159 9 ALTERNATIVE SEMANTICS FOR THREE-VALUED LOGIC 161
9.1 NUMERIC TRUTH-VALUES FOR THREE-VALUED LOGIC 161 9.2 ABSTRACT
ALGEBRAS FOR L 3 , K S3 , B^, AND B E3 163 9.3 MV-ALGEBRAS 167 9.4
EXERCISES 172 10 THE PRINCIPLE OF CHARITY RECONSIDERED AND A NEW PROBLEM
OF THE FRINGE 174 11 FUZZY PROPOSITIONAL LOGICS: SEMANTICS 176 11.1
FUZZY SETS AND DEGREES OF TRUTH 176 11.2 LUKASIEWICZ FUZZY PROPOSITIONAL
LOGIC 178 11.3 TAUTOLOGIES, CONTRADICTIONS, AND ENTAILMENT IN FUZZY
LOGIC 180 CONTENTS IX 11.4 AF-TAUTOLOGIES, DEGREE-ENTAILMENT, AND
JV-DEGREE-ENTAILMENT 183 11.5 FUZZY CONSEQUENCE 190 11.6 FUZZY
GENERALIZATIONS OF K S3 , B 3 , ANDB E3 ; THE EXPRESSIVE POWER OF FUZZY
L 192 11.7 T-NORMS, T-CONORMS, AND IMPLICATION IN FUZZY LOGIC 194 11.8
GODEL FUZZY PROPOSITIONAL LOGIC 199 11.9 PRODUCT FUZZY PROPOSITIONAL
LOGIC 202 11.10 FUZZY EXTERNAL ASSERTION AND NEGATION 203 11.11
EXERCISES 206 12 FUZZY ALGEBRAS 212 12.1 MORE ON MV-ALGEBRAS 212 12.2
RESIDUATED LATTICES AND BL-ALGEBRAS 214 12.3 ZERO AND UNIT PROJECTIONS
IN ALGEBRAIC STRUCTURES 219 12.4 EXERCISES 220 13 DERIVATION SYSTEMS FOR
FUZZY PROPOSITIONAL LOGIC 223 13.1 AN AXIOMATIC SYSTEM FOR TAUTOLOGIES
AND VALIDITY IN FUZZY L 223 13.2 A PAVELKA-STYLE DERIVATION SYSTEM FOR
FUZZY L 229 13.3 AN ALTERNATIVE AXIOMATIC SYSTEM FOR TAUTOLOGIES AND
VALIDITY IN FUZZY L , BASED ON BL-ALGEBRAS 245 13.4 AN AXIOMATIC SYSTEM
FOR TAUTOLOGIES AND VALIDITY IN FUZZYC 249 13.5 AN AXIOMATIC SYSTEM FOR
TAUTOLOGIES AND VALIDITY IN FUZZYP 252 13.6 SUMMARY: COMPARISION OF
FUZZY L , FUZZYC AND FUZZY P AND THEIR DERIVATION SYSTEMS 254 13.7
EXTERNAL ASSERTION AXIOMS 254 13.8 EXERCISES 256 14 FUZZY FIRST-ORDER
LOGICS: SEMANTICS 262 14.1 FUZZY INTERPRETATIONS 262 14.2 LUKASIEWICZ
FUZZY FIRST-ORDER LOGIC 263 14.3 TAUTOLOGIES AND OTHER SEMANTIC CONCEPTS
266 14.4 LUKASIEWICZ FUZZY LOGIC AND THE PROBLEMS OF VAGUENESS 268 14.5
GODEL FUZZY FIRST-ORDER LOGIC 278 14.6 PRODUCT FUZZY FIRST-ORDER LOGIC
280 14.7 THE SORITES PARADOX: COMPARISON OF FUZZY L V, FUZZY G V, AND
FUZZYPY 282 14.8 EXERCISES 282 15 DERIVATION SYSTEMS FOR FUZZY
FIRST-ORDER LOGIC 287 15.1 AXIOMATIC SYSTEMS FOR FUZZY FIRST-ORDER
LOGIC: OVERVIEW 287 15.2 A PAVELKA-STYLE DERIVATION SYSTEM FOR FUZZY L V
288 15.3 AN AXIOMATIC DERIVATION SYSTEM FOR FUZZYCV 294 CONTENTS 15.4
COMBINING FUZZY FIRST-ORDER LOGICAL SYSTEMS; EXTERNAL ASSERTION 297 15.5
EXERCISES 298 16 EXTENSIONS OF FUZZINESS 300 16.1 FUZZY QUALIFIERS:
HEDGES 300 16.2 FUZZY LINGUISTIC TRUTH-VALUES 303 16.3 OTHER FUZZY
EXTENSIONS OF FUZZY LOGIC 305 16.4 EXERCISES 306 17 FUZZY MEMBERSHIP
FUNCTIONS 309 17.1 DEFINING MEMBERSHIP FUNCTIONS 309 17.2 EMPIRICAL
CONSTRUCTION OF MEMBERSHIP FUNCTIONS 312 17.3 LOGICAL RELEVANCE? 313
17.4 EXERCISES 313 APPENDIX: BASICS OF COUNTABILITY AND UNCOUNTABILITY
315 BIBLIOGRAPHY 321 INDEX 327
|
| adam_txt |
AN INTRODUCTION TO MANY-VALUED AND FUZZY LOGIC SEMANTICS, ALGEBRAS, AND
DEBIATION SYSTEMS MERRIE BERGMANN EMERITA, SMITH COLLEGE CAMBRIDGE
UNIVERSITY PRESS CONTENTS PREFACE PAGE XI 1 INTRODUCTION 1.1 ISSUES OF
VAGUENESS 1 1.2 VAGUENESS DENNED 5 1.3 THE PROBLEM OF THE FRINGE 6 1.4
PREVIEW OF THE REST OF THE BOOK 7 1.5 HISTORY AND SCOPE OF FUZZY LOGIC 8
1.6 TALL PEOPLE 10 1.7 EXERCISES 10 2 REVIEW OF CLASSICAL PREPOSITIONAL
LOGIC 12 2.1 THE LANGUAGE OF CLASSICAL PROPOSITIONAL LOGIC 12 2.2
SEMANTICS OF CLASSICAL PROPOSITIONAL LOGIC 13 2.3 NORMAL FORMS 18 2.4 AN
AXIOMATIC DERIVATION SYSTEM FOR CLASSICAL PROPOSITIONAL LOGIC 21 2.5
FUNCTIONAL COMPLETENESS 32 2.6 DECIDABILITY 35 2.7 EXERCISES 36 3 REVIEW
OF CLASSICAL FIRST-ORDER LOGIC 39 3.1 THE LANGUAGE OF CLASSICAL
FIRST-ORDER LOGIC 39 3.2 SEMANTICS OF CLASSICAL FIRST-ORDER LOGIC 42 3.3
AN AXIOMATIC DERIVATION SYSTEM FOR CLASSICAL FIRST-ORDER LOGIC 49 3.4
EXERCISES 55 4 ALTERNATIVE SEMANTICS FOR TRUTH-VALUES AND
TRUTH-FUNCTIONS: NUMERIC TRUTH-VALUES AND ABSTRACT ALGEBRAS 57 4.1
NUMERIC TRUTH-VALUES FOR CLASSICAL LOGIC 57 4.2 BOOLEAN ALGEBRAS AND
CLASSICAL LOGIC 59 4.3 MORE RESULTS ABOUT BOOLEAN ALGEBRAS 63 **' * 4.4
EXERCISES 69 VIII CONTENTS 5 THREE-VALUED PROPOSITIONAL LOGICS:
SEMANTICS 71 5.1 KLEENE'S "STRONG" THREE-VALUED LOGIC . 71 5.2
LUKASIEWICZ'S THREE-VALUED LOGIC 76 5.3 BOCHVAR'S THREE-VALUED LOGICS 80
5.4 EVALUATING THREE-VALUED SYSTEMS; QUASI-TAUTOLOGIES AND
QUASI-CONTRADICTIONS 84 5.5 NORMAL FORMS 89 5.6 QUESTIONS OF
INTERDEFINABILITY BETWEEN THE SYSTEMS AND FUNCTIONAL COMPLETENESS 90 5.7
LUKASIEWICZ'S SYSTEM EXPANDED 94 5.8 EXERCISES 96 6 DERIVATION SYSTEMS
FOR THREE-VALUED PROPOSITIONAL LOGIC 100 6.1 AN AXIOMATIC SYSTEM FOR
TAUTOLOGIES AND VALIDITY IN THREE-VALUED LOGIC 100 6.2 A PAVELKA-STYLE
DERIVATION SYSTEM FOR L 3 114 6.3 EXERCISES 126 7 THREE-VALUED
FIRST-ORDER LOGICS: SEMANTICS 130 7.1 A FIRST-ORDER GENERALIZATION OF L
3 130 7.2 QUANTIFIERS BASED ON THE OTHER THREE-VALUED SYSTEMS 137 7.3
TAUTOLOGIES, VALIDITY, AND "QUASI-"SEMANTIC CONCEPTS 140 7.4 EXERCISES
143 8 DERIVATION SYSTEMS FOR THREE-VALUED FIRST-ORDER LOGIC 146 8.1 AN
AXIOMATIC SYSTEM FOR TAUTOLOGIES AND VALIDITY IN THREE-VALUED
FIRST-ORDER LOGIC 146 8.2 A PAVELKA-STYLE DERIVATION SYSTEM FOR L 3 V
153 8.3 EXERCISES 159 9 ALTERNATIVE SEMANTICS FOR THREE-VALUED LOGIC 161
9.1 NUMERIC TRUTH-VALUES FOR THREE-VALUED LOGIC 161 9.2 ABSTRACT
ALGEBRAS FOR L 3 , K S3 , B^, AND B E3 163 9.3 MV-ALGEBRAS 167 9.4
EXERCISES 172 10 THE PRINCIPLE OF CHARITY RECONSIDERED AND A NEW PROBLEM
OF THE FRINGE 174 11 FUZZY PROPOSITIONAL LOGICS: SEMANTICS 176 11.1
FUZZY SETS AND DEGREES OF TRUTH 176 11.2 LUKASIEWICZ FUZZY PROPOSITIONAL
LOGIC 178 11.3 TAUTOLOGIES, CONTRADICTIONS, AND ENTAILMENT IN FUZZY
LOGIC 180 CONTENTS IX 11.4 AF-TAUTOLOGIES, DEGREE-ENTAILMENT, AND
JV-DEGREE-ENTAILMENT 183 11.5 FUZZY CONSEQUENCE 190 11.6 FUZZY
GENERALIZATIONS OF K S3 , B' 3 , ANDB E3 ; THE EXPRESSIVE POWER OF FUZZY
L 192 11.7 T-NORMS, T-CONORMS, AND IMPLICATION IN FUZZY LOGIC 194 11.8
GODEL FUZZY PROPOSITIONAL LOGIC 199 11.9 PRODUCT FUZZY PROPOSITIONAL
LOGIC 202 11.10 FUZZY EXTERNAL ASSERTION AND NEGATION 203 11.11
EXERCISES 206 12 FUZZY ALGEBRAS 212 12.1 MORE ON MV-ALGEBRAS 212 12.2
RESIDUATED LATTICES AND BL-ALGEBRAS 214 12.3 ZERO AND UNIT PROJECTIONS
IN ALGEBRAIC STRUCTURES 219 12.4 EXERCISES 220 13 DERIVATION SYSTEMS FOR
FUZZY PROPOSITIONAL LOGIC 223 13.1 AN AXIOMATIC SYSTEM FOR TAUTOLOGIES
AND VALIDITY IN FUZZY L 223 13.2 A PAVELKA-STYLE DERIVATION SYSTEM FOR
FUZZY L 229 13.3 AN ALTERNATIVE AXIOMATIC SYSTEM FOR TAUTOLOGIES AND
VALIDITY IN FUZZY L , BASED ON BL-ALGEBRAS 245 13.4 AN AXIOMATIC SYSTEM
FOR TAUTOLOGIES AND VALIDITY IN FUZZYC 249 13.5 AN AXIOMATIC SYSTEM FOR
TAUTOLOGIES AND VALIDITY IN FUZZYP 252 13.6 SUMMARY: COMPARISION OF
FUZZY L , FUZZYC AND FUZZY P AND THEIR DERIVATION SYSTEMS 254 13.7
EXTERNAL ASSERTION AXIOMS 254 13.8 EXERCISES 256 14 FUZZY FIRST-ORDER
LOGICS: SEMANTICS 262 14.1 FUZZY INTERPRETATIONS 262 14.2 LUKASIEWICZ
FUZZY FIRST-ORDER LOGIC 263 14.3 TAUTOLOGIES AND OTHER SEMANTIC CONCEPTS
266 14.4 LUKASIEWICZ FUZZY LOGIC AND THE PROBLEMS OF VAGUENESS 268 14.5
GODEL FUZZY FIRST-ORDER LOGIC 278 14.6 PRODUCT FUZZY FIRST-ORDER LOGIC
280 14.7 THE SORITES PARADOX: COMPARISON OF FUZZY L V, FUZZY G V, AND
FUZZYPY 282 14.8 EXERCISES 282 15 DERIVATION SYSTEMS FOR FUZZY
FIRST-ORDER LOGIC 287 15.1 AXIOMATIC SYSTEMS FOR FUZZY FIRST-ORDER
LOGIC: OVERVIEW 287 15.2 A PAVELKA-STYLE DERIVATION SYSTEM FOR FUZZY L V
288 15.3 AN AXIOMATIC DERIVATION SYSTEM FOR FUZZYCV 294 CONTENTS 15.4
COMBINING FUZZY FIRST-ORDER LOGICAL SYSTEMS; EXTERNAL ASSERTION 297 15.5
EXERCISES 298 16 EXTENSIONS OF FUZZINESS 300 16.1 FUZZY QUALIFIERS:
HEDGES 300 16.2 FUZZY "LINGUISTIC" TRUTH-VALUES 303 16.3 OTHER FUZZY
EXTENSIONS OF FUZZY LOGIC 305 16.4 EXERCISES 306 17 FUZZY MEMBERSHIP
FUNCTIONS 309 17.1 DEFINING MEMBERSHIP FUNCTIONS 309 17.2 EMPIRICAL
CONSTRUCTION OF MEMBERSHIP FUNCTIONS 312 17.3 LOGICAL RELEVANCE? 313
17.4 EXERCISES 313 APPENDIX: BASICS OF COUNTABILITY AND UNCOUNTABILITY
315 BIBLIOGRAPHY 321 INDEX 327 |
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| ctrlnum | (OCoLC)263449385 (DE-599)BVBBV023335998 |
| dewey-full | 511.3/13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/13 |
| dewey-search | 511.3/13 |
| dewey-sort | 3511.3 213 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| format | Book |
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| index_date | 2024-07-02T20:59:41Z |
| indexdate | 2024-07-09T21:16:14Z |
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| language | English |
| lccn | 2007007725 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016519859 |
| oclc_num | 263449385 |
| open_access_boolean | |
| owner | DE-703 DE-19 DE-BY-UBM |
| owner_facet | DE-703 DE-19 DE-BY-UBM |
| physical | xii, 329 p. ill. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | Bergmann, Merrie Verfasser (DE-588)13627787X aut An introduction to many-valued and fuzzy logic semantics, algebras, and derivation systems Merrie Bergmann 1. publ. Cambridge Cambridge University Press 2008 xii, 329 p. ill. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 321-325) and index Fuzzy logic Many-valued logic Mehrwertige Logik (DE-588)4169335-8 gnd rswk-swf Fuzzy-Logik (DE-588)4341284-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Mehrwertige Logik (DE-588)4169335-8 s Fuzzy-Logik (DE-588)4341284-1 s DE-604 http://www.loc.gov/catdir/toc/ecip0711/2007007725.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0743/2007007725-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0743/2007007725-d.html Publisher description HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016519859&sequence=000005&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bergmann, Merrie An introduction to many-valued and fuzzy logic semantics, algebras, and derivation systems Fuzzy logic Many-valued logic Mehrwertige Logik (DE-588)4169335-8 gnd Fuzzy-Logik (DE-588)4341284-1 gnd |
| subject_GND | (DE-588)4169335-8 (DE-588)4341284-1 (DE-588)4123623-3 |
| title | An introduction to many-valued and fuzzy logic semantics, algebras, and derivation systems |
| title_auth | An introduction to many-valued and fuzzy logic semantics, algebras, and derivation systems |
| title_exact_search | An introduction to many-valued and fuzzy logic semantics, algebras, and derivation systems |
| title_exact_search_txtP | An introduction to many-valued and fuzzy logic semantics, algebras, and derivation systems |
| title_full | An introduction to many-valued and fuzzy logic semantics, algebras, and derivation systems Merrie Bergmann |
| title_fullStr | An introduction to many-valued and fuzzy logic semantics, algebras, and derivation systems Merrie Bergmann |
| title_full_unstemmed | An introduction to many-valued and fuzzy logic semantics, algebras, and derivation systems Merrie Bergmann |
| title_short | An introduction to many-valued and fuzzy logic |
| title_sort | an introduction to many valued and fuzzy logic semantics algebras and derivation systems |
| title_sub | semantics, algebras, and derivation systems |
| topic | Fuzzy logic Many-valued logic Mehrwertige Logik (DE-588)4169335-8 gnd Fuzzy-Logik (DE-588)4341284-1 gnd |
| topic_facet | Fuzzy logic Many-valued logic Mehrwertige Logik Fuzzy-Logik Lehrbuch |
| url | http://www.loc.gov/catdir/toc/ecip0711/2007007725.html http://www.loc.gov/catdir/enhancements/fy0743/2007007725-b.html http://www.loc.gov/catdir/enhancements/fy0743/2007007725-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016519859&sequence=000005&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bergmannmerrie anintroductiontomanyvaluedandfuzzylogicsemanticsalgebrasandderivationsystems |