Logic and its applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Prentice Hall
1996
|
| Edition: | 1. publ. |
| Series: | Prentice Hall international series in computer science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 310 S. graph. Darst. |
| ISBN: | 0130302635 |
Staff View
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| 250 | |a 1. publ. | ||
| 264 | 1 | |a London [u.a.] |b Prentice Hall |c 1996 | |
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Record in the Search Index
| _version_ | 1804125445798494208 |
|---|---|
| adam_text | LOGIC AND ITS APPLICATIONS EDMUND BURKE AND ERIC FOXLEY PRENTICE HALL
LONDON NEW YORK TORONTO SYDNEY TOKYO SINGAPORE MADRID MEXICO CITY MUNICH
CONTENTS PREFACE XIII PROPOSITIONAL LOGIC 1 1.1 INFORMAL INTRODUCTION 1
1.2 LOGICAL CONNECTIVES 2 1.2.1 NEGATION (NOT) 2 1.2.2 CONJUNCTION (AND)
2 1.2.3 DISJUNCTION (OR) 4 1.2.4 IMPLICATION 5 1.2.5 EQUIVALENCE 1 1.2.6
SUM AND PRODUCT NOTATIONS 1 1.2.7 PRIORITIES OF OPERATORS 8 1.3
TRUTH-TABLES OF FORMULAE 9 1.3.1 HOW TO CONSTRUCT THE TRUTH-TABLE OF A
FORMULA 9 1.3.2 IDENTICAL TRUTH-TABLES 11 1.3.3 INTERPRETATIONS AND
MODEIS 12 1.3.4 TAUTOLOGIES, ABSURDITIES AND MIXED FORMULAE 12 1.4 OTHER
LOGICAL CONNECTIVES 14 1.4.1 TRUTH FUNCTIONS 14 1.4.2 MONODIE OPERATORS
15 1.4.3 DYADIC OPERATORS 15 1.4.4 TRIADIC OPERATORS 17 1.4.5
REPRESENTING TRUTH FUNCTIONS IN TERMS OFDYADIC AND MONADIC OPERATORS 19
1.5 MANIPULATING PROPOSITIONAL FORMULAE 20 1.5.1 STANDARD IDENTITIES 20
1.5.2 COMPLETE SETS OF CONNECTIVES 21 1.5.3 OTHER COMPLETE SETS OF
CONNECTIVES 22 1.5.4 SHEFFER FUNCTIONS 23 V CONTENTS 1.5.5 NORMALFORMS
1.6 THE NEGATION OF PROPOSITIONAL FORMULAE 1.6.1 DEFINITION 1.6.2
GENERALIZED DE MORGAN S LAW 1.6.3 EXTENDED DISJUNCTION AND COENJUNCTION
1.6.4 DUALITY 1.7 ARGUMENTS AND ARGUMENT FORMS 1.7.1 SOME DEFINITIONS
ASSOCIATED WITH FORMULAE 1.7.2 SOME RULES FOR PROPOSITIONAL FORMULAE
1.7.3 THE VALIDITY OF AN ARGUMENT 1.7.4 MATHEMATICAL IF-AND-ONLY-IF
PROOFS 1.7.5 A THEOREM 1.7.6 ANOTHER THEOREM 1.8 SUMMARY 1.9 WORKED
EXAMPLES 1.10 EXERCISES FORMAL APPROACH TO PROPOSITIONAL LOGIC 2.1
INTRODUCTION 2.1.1 FORMAL SYSTEMS OF PROPOSITIONAL LOGIC 2.1.2 PROOFS
AND DEDUCTIONS 2.1.3 CONSTRUCTING FORMAL SYSTEMS 2.1.4 77IE RELATIONSHIP
BETWEEN FORMAL SYSTEMS AND INTERPRETATIONS 2.2 THE FORMAL PROPOSITIONAL
LOGIC SYSTEM L 2.2.1 THE CONSTRUCTION OF SYSTEM L 2.2.2 PROOFS IN SYSTEM
L 2.2.3 DEDUCTIONS IN SYSTEM L 2.2.4 DERIVED RULES OF INFERENCE IN
SYSTEM L 2.2.5 EXAMPLES 2.2.6 NOTATION FOR RULES 2.3 THE SOUNDNESS AND
COMPLETENESS THEOREMS FOR SYSTEM 2.3.1 INTRODUCTION 2.3.2 THE SOUNDNESS
THEOREM FOR SYSTEM L 2.3.3 THE COMPLETENESS THEOREM FOR SYSTEM L 2.4
INDEPENDENCE OF AXIOMS AND RULES 2.5 LEMMON S SYSTEM OF PROPOSITIONAL
LOGIC 2.5.1 AN INTRODUCTION TO THE SYSTEM 2.5.2 PROOFS AND DEDUCTIONS IN
LEMMON S SYSTEM 2.5.3 EXAMPLES OF DEDUCTIONS IN LEMMON S SYSTEM 2.6
SUMMARY 2.7 WORKED EXAMPLES 2.8 EXERCISES CONTENTS VII 3 APPLICATIONS TO
LOGIC DESIGN 3.1 3.2 3.3 3.4 3.5 3.6 3.7 INTRODUCTION SIMPLIFICATION
TECHNIQUES 3.2.1 A SIMPLE EXAMPLE 3.2.2 KARNAUGH MAPS 3.2.3
QUINE-MCCLUSKY MINIMIZATION UNIVERSAL DECISION ELEMENTS (UDES) 3.3.1
DEFINITION 3.3.2 A FEW FOUR-VARIABLE UNIVERSAL DECISION ELEMENTS LOGIC
DESIGN 3.4.1 BINARY ARITHMETIC ADDERS 3.4.2 SEQUENTIAL LOGIC SUMMARY
WORKED EXAMPLES EXERCISES 4 PREDICATE LOGIC 4.1 4.2 4.3 4.4 INFORMAL
INTRODUCTION 4.1.1 BACKGROUND 4.1.2 UNIVERSAL AND EXISTENTIAL
QUANTIFIERS 4.1.3 TRANSLATING BETWEEN FIRST-ORDER LANGUAGES AND THE
ENGLISH LANGUAGE 4.1.4 HINTS FOR TRANSLATING FROM ENGLISH TO LOGIC 4.1.5
EXAMPLES 4.1.6 SUMMARY 4.1.7 EXERCISES THE SEMANTICS OF PREDICATE LOGIC
4.2.1 FIRST-ORDER LANGUAGES 4.2.2 INTERPRETATIONS 4.2.3 SATISFACTION
4.2.4 TRUTH-TABLES OF INTERPRETATIONS 4.2.5 HERBRAND INTERPRETATIONS
4.2.6 SUMMARY 4.2.7 WORKED EXAMPLES 4.2.8 EXERCISES SYNTACTICAL SYSTEMS
OF PREDICATE LOGIC 4.3.1 THE SYSTEM K OF PREDICATE LOGIC 4.3.2
DISCUSSION OF THE SYSTEM K 4.3.3 FIRST-ORDER THEORIES 4.3.4 SUMMARY
4.3.5 WORKED EXAMPLE 4.3.6 EXERCISES SOUNDNESS AND COMPLETENESS 95 95 98
98 101 105 110 111 111 113 113 115 122 122 128 131 131 131 133 136 139
140 141 142 143 143 148 151 153 155 157 157 159 161 162 163 171 173 173
174 175 VIII CONTENTS 4.4.1 INTRODUCTION 175 4.4.2 THE SOUNDNESS OF
SYSTEM K 176 4.4.3 CONSISTENCY 180 4.4.4 THE COMPLETENESS OF SYSTEM K
180 4.4.5 SUMMARY 185 4.4.6 WORKED EXAMPLES 185 4.4.7 EXERCISES 188 5
LOGIC PROGRAMMING 190 5.1 INTRODUCTION 190 5.2 PROGRAMMING WITH
PROPOSITIONAL LOGIC 190 5.2.1 DEFINITIONS FOR PROPOSITIONAL LOGIC 190
5.2.2 PROPOSITIONAL RESOLUTION 191 5.2.3 REFUTATION AND DEDUCTIONS 193
5.2.4 NEGATION IN LOGIC PROGRAMMING 198 5.2.5 SLD-RESOLUTION 199 5.3
CLAUSAL FORM FOR PREDICATE LOGIC 202 5.3.1 PRENEXFORM 202 5.3.2 CLAUSAL
FORM 204 5.3.3 HOERN CLAUSES 206 5.4 THE SEMANTICS OF LOGIC PROGRAMMING
207 5.4.1 HOERN CLAUSES AND THEIR HERBRAND MODEIS 20 9 5.4.2 LOGIC
PROGRAMS AND THEIR HERBRAND MODEIS 210 5.4.3 LEAST HERBRAND MODEIS 210
5.4.4 CONSTRUCTION OF LEAST HERBRAND MODEIS 211 5.5 UNIFICATION AND
ANSWER SUBSTITUTIONS 214 5.5.1 SUBSTITUTIONS 214 5.5.2 UNIFICATION 216
5.5.3 PRACTICALITIES 218 5.6 PROGRAMMING WITH PREDICATE LOGIC 219 5.6.1
THE RESOLUTION RULE 219 5.6.2 THE PROOF STRATEGY OF PROLOG:
SLD-RESOLUTION 219 5.6.3 NEGATION IN LOGIC PROGRAMMING: THE CLOSED-WORLD
ASSUMPTION 222 5.7 CONCLUDING REMARKS 223 5.8 WORKED EXAMPLES 224 5.9
EXERCISES 228 6 FORMAL SYSTEM SPECIFICATION 232 6.1 INTRODUCTION 232
6.1.1 A SIMPLE EXAMPLE 233 6.1.2 A STATE SCHEMA 233 6.1.3 OPERATIONS OR
EVENTS AND THEIR SCHEMA 235 CONTENTS IX 6.1.4 PRE-AND POST-CONDITIONS
241 6.2 NOTATIONAL DIFFERENCES 241 6.3 THE Z SPECIFICATION LANGUAGE 243
6.3.1 BASIC TYPE DEFINITIONS 244 6.3.2 FREE TYPE DEFINITIONS 244 6.3.3
SCHEMA INCLUSION 245 6.3.4 SCHEMA TYPES 245 6.3.5 EXAMPLE: A COMPUTER
FILE SYSTEM 249 6.3.6 AXIOM SCHEMA 255 6.4 SCHEMA ALGEBRA 256 6.4.1
LINEARNOTATION 256 6.4.2 SCHEMA EXTENSION 256 6.4.3 SOME OTHER TYPES OF
DEFINITION 256 6.4.4 SCHEMA INCLUSION 257 6.4.5 THE TUPLE AND PRED
OPERATORS 257 6.4.6 ORNAMENTATION OF SCHEMA NAMES 257 6.4.7 LOGICAL
OPERATIONS ON SCHEMA 257 6.4.8 SCHEMA QUANTIFICATION 258 6.4.9
IDENTIFIER RENAMING 259 6.4.10 IDENTIFIER HIDING 259 6.4.11 SCHEMA
PRE-CONDITION 260 6.4.12 SCHEMA COMPOSITION 260 6.4.13 SCHEMA PIPING 262
6.4.14 AXIOMATIC DESCRIPTIONS 26 3 6.5 SUMMARY 263 6.6 WORKED EXAMPLES
264 6.6.1 SOME SIMPLE EXAMPLES 264 6.6.2 CASE STUDY: A VIDEO-RENTAL SHOP
271 6.6.3 CASE STUDY: A CAR-FERRY TERMINAL 214 6.7 EXERCISES 282
APPENDIX A: MATHEMATICAL BACKGROUND 284 AI INDUCTION PROOFS 284 A2 SET
THEORY 286 A2.1 COMPREHENSIVE SPECIFICATION OF A SET 286 A2.2 OPERATIONS
INVOLVING SETS 287 A3 BAGS 288 A4 RELATIONS 289 A4.1 DOMAIN AND RAENGE
289 A4.2 COMPOSITION 290 A4.3 DOMAIN AND RAENGE OPERATIONS 290 A4.4
OVERRIDE OPERATION 292 A4.5 SET IMAGE 292 X CONTENTS 293 294 295 297 297
297 300 300 APPENDIX C: SYMBOLS USED IN THE BOOK 302 A5 A6 A4.6
EQUIVALENCE RELATIONS FUNCTIONS SEQUENCES APPENDIX B: OTHER NOTATIONS BL
B2 B3 B4 ALTERNATIVE NOTATIONS POLISH NOTATION WORKED EXAMPLES EXERCISES
INDEX 305
|
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| author | Burke, Edmund K. 1964- Foxley, Eric |
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| dewey-full | 511.3 005.131 511.320 |
| dewey-hundreds | 500 - Natural sciences and mathematics 000 - Computer science, information, general works |
| dewey-ones | 511 - General principles of mathematics 005 - Computer programming, programs, data, security |
| dewey-raw | 511.3 005.131 511.3 20 |
| dewey-search | 511.3 005.131 511.3 20 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| edition | 1. publ. |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:01:41Z |
| institution | BVB |
| isbn | 0130302635 |
| language | English |
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| spelling | Burke, Edmund K. 1964- Verfasser (DE-588)124111068 aut Logic and its applications Edmund Burke and Eric Foxley 1. publ. London [u.a.] Prentice Hall 1996 XVIII, 310 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Prentice Hall international series in computer science Kunstmatige intelligentie gtt Logisch programmeren gtt Predicatenlogica gtt Logic programming Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 Foxley, Eric Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007330171&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Burke, Edmund K. 1964- Foxley, Eric Logic and its applications Kunstmatige intelligentie gtt Logisch programmeren gtt Predicatenlogica gtt Logic programming Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 |
| title | Logic and its applications |
| title_auth | Logic and its applications |
| title_exact_search | Logic and its applications |
| title_full | Logic and its applications Edmund Burke and Eric Foxley |
| title_fullStr | Logic and its applications Edmund Burke and Eric Foxley |
| title_full_unstemmed | Logic and its applications Edmund Burke and Eric Foxley |
| title_short | Logic and its applications |
| title_sort | logic and its applications |
| topic | Kunstmatige intelligentie gtt Logisch programmeren gtt Predicatenlogica gtt Logic programming Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Kunstmatige intelligentie Logisch programmeren Predicatenlogica Logic programming Logic, Symbolic and mathematical Mathematische Logik |
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