Boolean reasoning the logic of Boolean equations
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| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston u.a.
Kluwer
1990
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| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Brown, Frank M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Boolean reasoning |b the logic of Boolean equations |c by Frank Markham Brown |
| 264 | 1 | |a Boston u.a. |b Kluwer |c 1990 | |
| 300 | |a XVIII, 273 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Boole, Algèbre de | |
| 650 | 7 | |a Boole, Algèbre de |2 ram | |
| 650 | 7 | |a algebre booleenne |2 inriac | |
| 650 | 7 | |a analyse booleenne |2 inriac | |
| 650 | 7 | |a equation booleenne |2 inriac | |
| 650 | 7 | |a raisonnement booleen |2 inriac | |
| 650 | 7 | |a raisonnement syllogistique |2 inriac | |
| 650 | 4 | |a Algebra, Boolean | |
| 650 | 0 | 7 | |a Boolesche Algebra |0 (DE-588)4146280-4 |2 gnd |9 rswk-swf |
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| 689 | 1 | 1 | |a Boolesche Algebra |0 (DE-588)4146280-4 |D s |
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Datensatz im Suchindex
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|---|---|
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| DE-BY-TUM_location | LSB |
| DE-BY-TUM_media_number | TEMP2962114 |
| _version_ | 1820888362795401216 |
| adam_text | BOOLEAN REASONING THE LOGIC OF BOOLEAN EQUATIONS BY FRANK MARKHAM BROWN
AIR FORCE INSTITUTE OF TECHNOLOGY FF KLUWER ACADEMIC PUBLISHERS
BOSTON/DORDRECHT/LONDON CONTENTS PREFACE XI TWO LOGICAL LANGUAGES XI
BOOLEAN REASONING XII BOOLEAN ALGEBRA AND SWITCHING THEORY XIII AN
APPROACH TO BOOLEAN PROBLEM-SOLVING XIV BOOLEAN REASONING VS. PREDICATE
LOGIC XV OUTLINE XVI ACKNOWLEDGMENTS XVIII 1 FUNDAMENTAL CONCEPTS 1 1.1
FORMULAS 1 1.2 PROPOSITIONS AND PREDICATES 2 1.3 SETS 5 1.4 OPERATIONS
ON SETS 9 1.5 PARTITIONS 11 1.6 RELATIONS 11 1.7 FUNCTIONS 16 1.8
OPERATIONS AND ALGEBRAIC SYSTEMS 18 2 BOOLEAN ALGEBRAS 23 2.1 POSTULATES
FOR A BOOLEAN ALGEBRA 23 2.2 EXAMPLES OF BOOLEAN ALGEBRAS 24 2.2.1 THE
ALGEBRA OF CLASSES (SUBSETS OF A SET) 24 2.2.2 THE ALGEBRA OF
PROPOSITIONAL FUNCTIONS 25 2.2.3 ARITHMETIC BOOLEAN ALGEBRAS 26 2.2.4
THE TWO-ELEMENT BOOLEAN ALGEBRA 26 2.2.5 SUMMARY OF EXAMPLES 26 2.3 THE
STONE REPRESENTATION THEOREM 27 V VI CONTENTS 2.4 THE INCLUSION-RELATION
28 2.4.1 INTERVALS 30 2.5 SOME USEFUL PROPERTIES 30 2.6 N-VARIABLE
BOOLEAN FORMULAS 33 2.7 N-VARIABLE BOOLEAN FUNCTIONS 34 2.8 BOOLE S
EXPANSION THEOREM 36 2.9 THE MINTERM CANONICAL FORM 39 2.9.1
TRUTH-TABLES 41 2.9.2 MAPS 42 2.10 THE LOEWENHEIM-MUELLER VERIFICATION
THEOREM 44 2.11 SWITCHING FUNCTIONS 45 2.12 INCOMPLETELY-SPECIFIED
BOOLEAN FUNCTIONS 45 2.13 BOOLEAN ALGEBRAS OF BOOLEAN FUNCTIONS 47
2.13.1 FREE BOOLEAN ALGEBRAS 48 2.14 ORTHONORMAL EXPANSIONS 48 2.14.1
LOEWENHEIM S EXPANSIONS 50 2.15 BOOLEAN QUOTIENT 53 2.16 THE BOOLEAN
DERIVATIVE 56 2.17 RECURSIVE DEFINITION OF BOOLEAN FUNCTIONS 58 2.18
WHAT GOOD ARE BIG BOOLEAN ALGEBRAS? 60 3 THE BLAKE CANONICAL FORM 71
3.1 DEFINITIONS AND TERMINOLOGY 72 3.2 SYLLOGISTIC & BLAKE CANONICAL
FORMULAS 73 3.3 GENERATION OF BCF(F) 75 3.4 EXHAUSTION OF IMPLICANTS 76
3.5 ITERATED CONSENSUS 77 3.5.1 QUINE S METHOD 78 3.5.2 SUCCESSIVE
EXTRACTION 80 3.6 MULTIPLICATION 80 3.6.1 RECURSIVE MULTIPLICATION 81
3.6.2 COMBINING MULTIPLICATION AND ITERATED CONSENSUS ... 83 3.6.3
UNWANTED SYLLOGISTIC FORMULAS 85 CONTENTS VII 4 BOOLEAN ANALYSIS 87 4.1
REVIEW OF ELEMENTARY PROPERTIES 87 4.2 BOOLEAN SYSTEMS 88 4.2.1
ANTECEDENT, CONSEQUENT, AND EQUIVALENT SYSTEMS ... 89 4.2.2 SOLUTIONS 89
4.3 REDUCTION 89 4.4 THE EXTENDED VERINCATION THEOREM 91 4.5 PORETSKY S
LAW OF FORMS 92 4.6 BOOLEAN CONSTRAINTS 93 4.7 ELIMINATION 95 4.8
ELIMINANTS 100 4.9 RUDUNDANT VARIABLES 107 4.10 SUBSTITUTION 113 4.11
THE TAUTOLOGY PROBLEM 115 4.11.1 TESTING FOR TAUTOLOGY 115 4.11.2 THE
SUM-TO-ONE THEOREM 116 4.11.3 NEARLY-MINIMAL SOP FORMULAS 117 5
SYLLOGISTIC REASONING 123 5.1 THE PRINCIPLE OF ASSERTION 124 5.2
DEDUCTION BY CONSENSUS 126 5.3 SYLLOGISTIC FORMULAS 127 5.4 CLAUSAL FORM
129 5.5 PRODUCING AND VERIFYING CONSEQUENTS 132 5.5.1 PRODUCING
CONSEQUENTS 132 5.5.2 VERIFYING CONSEQUENTS 133 5.5.3 COMPARISON OF
CLAUSES 134 5.6 CLASS-LOGIC 134 5.7 SELECTIVE DEDUCTION 136 5.8
FUNCTIONAL RELATIONS 138 5.9 DEPENDENT SETS OF FUNCTIONS 140 5.10
SUM-TO-ONE SUBSETS 143 5.11 IRREDUNDANT FORMULAS 145 VIII CONTENTS 6
SOLUTION OF BOOLEAN EQUATIONS 153 6.1 PARTICULAR SOLUTIONS AND
CONSISTENCY 154 6.2 GENERAL SOLUTIONS 156 6.3 SUBSUMPTIVE GENERAL
SOLUTIONS 158 6.3.1 SUCCESSIVE ELIMINATION 159 6.3.2 DERIVING ELIMINANTS
FROM MAPS 161 6.3.3 RECURRENT COVERS AND SUBSUMPTIVE SOLUTIONS 162 6.3.4
SIMPLIFIED SUBSUMPTIVE SOLUTIONS 166 6.3.5 SIMPLIFICATION VIA MARQUAND
DIAGRAMS 167 6.4 PARAMETRIC GENERAL SOLUTIONS 167 6.4.1 SUCCESSIVE
ELIMINATION 169 6.4.2 PARAMETRIC SOLUTIONS BASED ON RECURRENT COVERS . .
. 172 6.4.3 LOEWENHEIM S FORMULA 175 7 FUNCTIONAL DEDUCTION 181 7.1
FUNCTIONALLY DEDUCIBLE ARGUMENTS 182 7.2 ELIMINABLE AND DETERMINING
SUBSETS 187 7.2.1 U-ELIMINABLE SUBSETS 187 7.2.2 -DETERMINING SUBSETS
189 7.2.3 CALCULATION OF MINIMAL -DETERMINING SUBSETS . . . . 190 8
BOOLEAN IDENTIFICATION 193 8.1 PARAMETRIC AND DIAGNOSTIC MODELS 195
8.1.1 PARAMETRIC MODELS 195 8.1.2 THE DIAGNOSTIC AXIOM 197 8.1.3
DIAGNOSTIC EQUATIONS AND FUNCTIONS 197 8.1.4 AUGMENTATION 199 8.2
ADAPTIVE IDENTIFICATION 201 8.2.1 INITIAL AND TERMINAL SPECIFICATIONS
201 8.2.2 UPDATING THE MODEL 204 8.2.3 EFFECTIVE INPUTS 205 8.2.4
TEST-PROCEDURE 208 CONTENTS IX 9 RECURSIVE REAIIZATIONS OF COMBINATIONAL
CIRCUITS 211 9.1 THE DESIGN-PROCESS 212 9.2 SPECIFICATIONS 213 9.2.1
SPECIFICATION-FORMATS 214 9.2.2 CONSISTENT SPECIFICATIONS 218 9.3
TABULAR SPECIFICATIONS 219 9.4 STRONGLY COMBINATIONAL SOLUTIONS 223 9.5
LEAST-COST RECURSIVE SOLUTIONS 224 9.6 CONSTRUCTING RECURSIVE SOLUTIONS
229 9.6.1 THE PROCEDURA 232 9.6.2 AN IMPLEMENTATION USING BORIS 234 A
SYLLOGISTIC FORMULAS 239 A.L ABSORPTIVE FORMULAS 240 A.2 SYLLOGISTIC
FORMULAS 240 A.3 PRIME IMPLICANTS 244 A.4 THE BLAKE CANONICAL FORM 245
BIBLIOGRAPHY 247 INDEX 265
|
| any_adam_object | 1 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 130 SK 150 |
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| ctrlnum | (OCoLC)21558236 (DE-599)BVBBV004302135 |
| dewey-full | 511.3/24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/24 |
| dewey-search | 511.3/24 |
| dewey-sort | 3511.3 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004302135 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T11:11:34Z |
| institution | BVB |
| isbn | 0792391217 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002675545 |
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| owner_facet | DE-12 DE-739 DE-20 DE-91 DE-BY-TUM DE-29T DE-11 DE-188 |
| physical | XVIII, 273 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Kluwer |
| record_format | marc |
| spellingShingle | Brown, Frank M. Boolean reasoning the logic of Boolean equations Boole, Algèbre de Boole, Algèbre de ram algebre booleenne inriac analyse booleenne inriac equation booleenne inriac raisonnement booleen inriac raisonnement syllogistique inriac Algebra, Boolean Boolesche Algebra (DE-588)4146280-4 gnd Logik (DE-588)4036202-4 gnd |
| subject_GND | (DE-588)4146280-4 (DE-588)4036202-4 |
| title | Boolean reasoning the logic of Boolean equations |
| title_auth | Boolean reasoning the logic of Boolean equations |
| title_exact_search | Boolean reasoning the logic of Boolean equations |
| title_full | Boolean reasoning the logic of Boolean equations by Frank Markham Brown |
| title_fullStr | Boolean reasoning the logic of Boolean equations by Frank Markham Brown |
| title_full_unstemmed | Boolean reasoning the logic of Boolean equations by Frank Markham Brown |
| title_short | Boolean reasoning |
| title_sort | boolean reasoning the logic of boolean equations |
| title_sub | the logic of Boolean equations |
| topic | Boole, Algèbre de Boole, Algèbre de ram algebre booleenne inriac analyse booleenne inriac equation booleenne inriac raisonnement booleen inriac raisonnement syllogistique inriac Algebra, Boolean Boolesche Algebra (DE-588)4146280-4 gnd Logik (DE-588)4036202-4 gnd |
| topic_facet | Boole, Algèbre de algebre booleenne analyse booleenne equation booleenne raisonnement booleen raisonnement syllogistique Algebra, Boolean Boolesche Algebra Logik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002675545&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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