Classical and fuzzy concepts in mathematical logic and applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
1998
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 364 S. |
| ISBN: | 0849331978 |
Staff View
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Record in the Search Index
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| adam_text | CLASSICAL AND FUZZY CONCEPTS IN MATHEMATICAL LOGIC AND APPLICATIONS
MIRCEA REGHI§ EUGENE ROVENTA CRC PRESS BOCA RATON BOSTON LONDON NEW YORK
WASHINGTON, D.C. CONTENTS INTRODUCTION TO NAIVE MATHEMATICAL LOGIC I
PROPOSITIONAL LOGIC 15 1 THE FORMAL LANGUAGE OF PROPOSITIONAL LOGIC 23
1.1 THE FORMAL LANGUAGE CO OF PROPOSITIONAL LOGIC USING PAREN- THESES 23
1.2 THE FORMAL LANGUAGE OF PROPOSITIONAL LOGIC WITHOUT PAREN- THESES
(POLISH NOTATION) 27 2 THE TRUTH STRUCTURE ON 0 IN SEMANTIC VERSION 37
2.1 BOOLEAN INTERPRETATIONS OF THE LANGUAGE CO 37 2.2 SEMANTIC DEDUCTION
51 2.3 THE SEMANTIC LINDENBAUM ALGEBRA OF O 63 3 THE TRUTH STRUCTURE ON
C O IN THE SYNTACTIC VERSION 69 3.1 THE SYSTEM OF HILBERT H: AXIOMS,
INFERENCE, THEOREMS . . 69 3.2,. METATHEOREMS 72 3.3 THE SYNTACTIC
LINDENBAUM ALGEBRA OF CO- NORMAL FORMULAS 88 4 CONNECTIONS BETWEEN THE
TRUTH STRUCTURES ON CO IN SEMANTIC AND SYNTACTIC VERSIONS 97 4.1 ALL
THEOREMS ARE TAUTOLOGIES (SOUNDNESS OF PROPOSITIONAL LOGIC) 97 4.2 ALL
TAUTOLOGIES ARE THEOREMS (COMPLETENESS OF PROPOSITIONAL LOGIC) 100 4.3
ANOTHER PROOF OF THE COMPLETENESS METATHEOREM 104 5 OTHER SYNTACTIC
VERSIONS OF THE TRUTH STRUCTURE ON 0 107 5.1 SYSTEMS L AND M:
EQUIVALENCE TO THE SYSTEM H 107 5.2 SOME REMARKS ABOUT THE INDEPENDENCE
OF AXIOMS 121 5.3 SYSTEM C OF LUKASIEWICZ AND TARSKI 127 6 ELEMENTS OF
FUZZY PROPOSITIONAL LOGIC 131 6.1 SOME ELEMENTARY NOTIONS ABOUT FUZZY
SETS 132 6.2 THE LANGUAGE OF FUZZY PROPOSITIONAL LOGIC 135 6.3 THE
SEMANTIC TRUTH STRUCTURE OF FUZZY PROPOSITIONAL LOGIC 136 6.4 ELEMENTS
OF FUZZY PROPOSITIONAL LOGIC IN THE SYNTACTIC VERSIONL45 7 APPLICATIONS
OF PROPOSITIONAL LOGIC IN COMPUTER SCIENCE 153 7.1 RECALL LINDENBAUM
ALGEBRA OF THE LANGUAGE O 153 7.2 SOME CONNECTIONS OF 0 WITH
PROGRAMMING LANGUAGES . . . 156 7.3 KARNAUGH MAPS 157 7.4 SWITCHING
NETWORKS 159 7.5 LOGICAL NETWORKS 175 EXERCISES (PART I) 178 II
PREDICATE LOGIC 183 8 INTRODUCTORY CONSIDERATIONS 187 9 THE FORMAL
LANGUAGE OF PREDICATE LOGIC 197 9.1 THE FORMAL ALPHABET OF PREDICATE
LOGIC: FORMAL WORDS . . 197 9.2 TERMS AND FORMULAS * 201 10 THE SEMANTIC
TRUTH STRUCTURE ON THE LANGUAGE C OF PREDICATE LOGIC 205 10.1 THE NOTION
OF INTERPRETATION OF THE LANGUAGE C 205 10.2 SEMANTIC DEDUCTION IN
PREDICATE LOGIC 221 11 THE SYNTACTIC TRUTH STRUCTURE ON THE LANGUAGE C
OF PREDICATE LOGIC 233 11.1 AXIOMS, THEOREMS 233 11.2 SOME REMARKABLE
METATHEOREMS 237 11.3 COMPLETENESS OF PREDICATE LOGIC 243 12 ELEMENTS OF
FUZZY PREDICATE LOGIC 259 12.1 THE LANGUAGE OF FUZZY PREDICATE LOGIC 259
12.2 THE SEMANTIC TRUTH STRUCTURE OF FUZZY PREDICATE LOGIC . . 261 12.3
THE SYNTACTIC TRUTH STRUCTURE OF FUZZY PREDICATE LOGIC . . 265 13
FURTHER APPLICATIONS OF LOGIC IN COMPUTER SCIENCE 273 13.1 ELEMENTS OF
THE THEORY OF RESOLUTION 273 13.2 ELEMENTS OF LOGICAL FOUNDATIONS OF
PROLOG 296 13.3 ELEMENTS OF APPROXIMATE REASONING FOR EXPERT SYSTEMS
DESIGN 306 EXERCISES (PART II) 315 A BOOLEAN ALGEBRAS 321 A.I BOOLEAN
ALGEBRAS. DEFINITIONS. EXAMPLES 321 A.2 ATOMS, ATOMIC AND FINITE BOOLEAN
ALGEBRAS 325 A.3 BOOLEAN ALGEBRA OF BOOLEAN FUNCTIONS 336 B MV-ALGEBRAS
339 B.I DEFINITIONS OF MV-ALGEBRAS, BASIC PROPERTIES; EXAMPLES . . 339
B.2 MV-SUBALGEBRAS AND HOMOMORPHISMS OF MV-ALGEBRAS . . . 344 B.3 FINITE
MV-ALGEBRAS 346 C GENERAL CONSIDERATIONS ABOUT FUZZY SETS 351 C.I
INTRODUCTION TO FUZZY SET THEORY . . 351 C.2 BASIC DEFINITIONS AND
EXAMPLES 354 REFERENCES 359 INDEX 363
|
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| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| format | Book |
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| institution | BVB |
| isbn | 0849331978 |
| language | English |
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| physical | 364 S. |
| publishDate | 1998 |
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| publishDateSort | 1998 |
| publisher | CRC Press |
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| spelling | Reghiş, Mircea Verfasser (DE-588)1138805254 aut Classical and fuzzy concepts in mathematical logic and applications Mircea Reghiş ; Eugene Roventa Boca Raton [u.a.] CRC Press 1998 364 S. txt rdacontent n rdamedia nc rdacarrier Fuzzy logic Logic, Symbolic and mathematical Fuzzy-Logik (DE-588)4341284-1 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Fuzzy-Logik (DE-588)4341284-1 s DE-604 Mathematische Logik (DE-588)4037951-6 s Roventa, Eugene Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008173680&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reghiş, Mircea Roventa, Eugene Classical and fuzzy concepts in mathematical logic and applications Fuzzy logic Logic, Symbolic and mathematical Fuzzy-Logik (DE-588)4341284-1 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4341284-1 (DE-588)4037951-6 |
| title | Classical and fuzzy concepts in mathematical logic and applications |
| title_auth | Classical and fuzzy concepts in mathematical logic and applications |
| title_exact_search | Classical and fuzzy concepts in mathematical logic and applications |
| title_full | Classical and fuzzy concepts in mathematical logic and applications Mircea Reghiş ; Eugene Roventa |
| title_fullStr | Classical and fuzzy concepts in mathematical logic and applications Mircea Reghiş ; Eugene Roventa |
| title_full_unstemmed | Classical and fuzzy concepts in mathematical logic and applications Mircea Reghiş ; Eugene Roventa |
| title_short | Classical and fuzzy concepts in mathematical logic and applications |
| title_sort | classical and fuzzy concepts in mathematical logic and applications |
| topic | Fuzzy logic Logic, Symbolic and mathematical Fuzzy-Logik (DE-588)4341284-1 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Fuzzy logic Logic, Symbolic and mathematical Fuzzy-Logik Mathematische Logik |
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