Verfügbarkeit: Symbolic logic | Technische Universität München

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Bibliographische Detailangaben
Beteilige Person:	Agler, David W. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Lanham, Md. [u.a.] Rowman & Littlefield Publishers 2013
Schlagwörter:	aLogic, Modern aLogic, Symbolic and mathematical Mathematische Logik
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025748503&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025748503&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Includes bibliographical references (p. ) and index
Umfang:	XIX, 375 S.
ISBN:	9781442217423 9781442217416

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Datensatz im Suchindex

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adam_text	IMAGE 1 EXTENDED TABLE OF CONTENTS ACKNOWLEDGMENTS INTRODUCTION 1.1 WHAT JS SYMBOLIC LOGIC? 1.2 WHY STUDY LOGIC? 1.3 HOW DO 1STUDY LOGIC? 1.4 HOW JS THE BOOK STRUCTURED? T PROPOSITIONS, ARGUMENTS, AND LOGICAL PROPERTIES I. 1 PROPOSITIONS 1.2 ARGUMENTS 1.2.1 WHAT IS AN ARGUMENT? 1.2.2 IDENTIFYING ARGUMENTS 1.2.3 ARGUMENT INDICATORS 1.2.4 TYPES OF ARGUMENTS EXERCISE SET # 1 SOLUTIONS TO STARRED EXERCISES FROM EXERCISE SET # 1 1.3 DEDUCTIVELY VALID ARGUMENTS 1.3.1 DEDUCTIVE VALIDITY DEFINED 1.3.2 TESTING FOR DEDUCTIVE VALIDITY 1.4 SUMMARY END-OF-CHAPTER EXERCISES SOLUTIONS TO STARRED EXERCISES FROM END-OF-CHAPTER EXERCISES DEFINITIONS IX XIX 1 1 2 2 5 5 7 7 8 9 10 12 14 14 14 17 20 20 22 23 IMAGE 2 X EXTENDED TABLE OFCONTENTS 2 LANGUAGE, SYNTAX, AND SEMANTICS 25 2.1 TRUTH FUNCTIONS 25 2.2 THE SYMBOLS OF PL AND TRUTH-FUNCTIONAL OPERATORS 29 2.2.1 CONJUNCTION 30 2.2.2 NEGATION 32 2.2.3 SCOPE INDICATORS AND THE MAIN OPERATOR 33 2.3 SYNTAX OF PL 38 2.3.1 METALANGUAGE, OBJECT LANGUAGE, USE, AND MENTION 38 2.3.2 METAVARIABLES, LITERAL NEGATION, AND THE MAIN OPERATOR 39 2.3.3 THE LANGUAGE AND SYNTAX OF PL 41 2.3.4 LITERAL NEGATION AND THE MAIN OPERATOR 42 EXERCISE SET # I 43 SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET # 1 45 2.4 DISJUNCTION, CONDITIONAL, BICONDITIONAL 45 2.4.1 DISJUNCTION 46 2.4.2 MATERIAL CONDITIONAL 48 2.4.3 MATERIAL BICONDITIONAL 51 2.5 ADVANCED TRANSLATION 52 END-OF-CHAPTER EXERCISES 58 SOLUTIONS TO STARRED EXERCISES IN END-OF-CHAPTER EXERCISES 60 DEFINITIONS 62 GUIDE TO TRANSLATION FROM ENGLISH TO PL 62 3 TRUTH TABLES 65 3.1 VALUATIONS (TRUTH-VALUE ASSIGNMENTS) 65 EXERCISE SET # 1 68 SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET # 1 69 3.2 TRUTH TABLES FOR PROPOSITIONS 69 EXERCISE SET #2 74 SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET #2 75 3.3 TRUTH TABLE ANALYSIS OF PROPOSITIONS 76 3.3.1 TAUTOLOGY 76 3.3.2 CONTRADICTION 77 3.3.3 CONTINGENCY 78 EXERCISE SET #3 80 SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET #3 80 IMAGE 3 EXTENDED TABLE OFCONTENTS XI 3.4 TRUTH TABLE ANALYSIS OF SETS OF PROPOSITIONS 81 3.4.1 EQUIVALENEE 81 3.4.2 CONSISTENEY 82 3.5 THE MATERIAL CONDITIONAL EXPLAINED (OPTIONAL) 84 3.6 TRUTH TABLE ANALYSIS OF ARGUMENTS 88 3.6.1 VALIDITY 88 3.6.2 VALIDITY AND INEONSISTENEY 89 3.7 SHORT TRUTH TABLE TEST FOR INVALIDITY 91 END-OF-CHAPTER EXERCISES 92 SOLUTIONS TO STARRED EXEREISES IN END-OF-CHAPTER EXERCISES 95 DEFINITIONS 96 4 TRUTH TREES 99 4.1 TRUTH- TREE SETUP AND BASIES IN DEEOMPOSITION 99 4.1.1 TRUTH- TREE SETUP 100 4.1.2 TRUTH- TREE DEEOMPOSITION 100 EXEREISE SET # 1 104 4.2 TRUTH- TREE DEEOMPOSITION RULES 105 4.2.1 CONJUNETION DEEOMPOSITION RULE (I D) 105 4.2.2 DISJUNETION DEEOMPOSITION RULE (VD) 107 4.2.3 DEEOMPOSE PROPOSITIONS UNDER EVERY DESCENDING OPEN BRANEH 115 EXERCISE SET #2 118 SOLUTIONS TO STARRED EXERCISES IN EXEREISE SET #2 119 4.3 THE REMAINING DECOMPOSITION RULES 120 4.3.1 CONDITIONAL DEEOMPOSITION (~D) 120 4.3.2 BIEONDITIONAL DEEOMPOSITION (HD) 121 4.3.3 NEGATED CONJUNETION DEEOMPOSITION (-,I D) 122 4.3.4 NEGATED DISJUNETION DEEOMPOSITION (-,YD) 123 4.3.5 NEGATED CONDITIONAL DEEOMPOSITION (-,~D) 123 4.3.6 NEGATED BIEONDITIONAL DEEOMPOSITION (-,HD) 123 4.3.7 DOUBLE NEGATION DEEOMPOSITION (...,...,D) 124 4.3.8 TRUTH- TREE RULES 125 EXEREISE SET #3 125 SOLUTIONS TO STARRED EXERCISES IN EXEREISE SET #3 126 4.4 BASIE STRATEGIES 127 4.4.1 STRATEGIE RULE 1 127 4.4.2 STRATEGIE RULE 2 128 IMAGE 4 XII EXTENDED TAB/E OFCONTENTS 4.4.3 STRATEGIE RULE 3 4.4.4 STRATEGIE RULE 4 EXEREISE SET #4 SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET #4 4.5 TRUTH- TREE WALK THROUGH 4.6 LOGICAL PROPERTIES OFTRUTH TREES 4.6.1 SEMANTIE ANALYSIS OF TRUTH TREES EXERCISE SET #5 SOLUTIONS TO STARRED EXEREISES IN EXEREISE SET #5 4.6.2 CONSISTENEY 4.6.3 TAUTOLOGY, CONTRADIETION, AND CONTINGENEY 4.6.4 LOGIEAL EQUIVALENEE 4.6.5 VALIDITY END-OF-CHAPTER EXEREISES SOLUTIONS TO STARRED EXERCISES IN END-OF-CHAPTER EXERCISES DEFINITIONS TRUTH-TREE VOEABULARY KEY FOR TRUTH- TREE ANALYSIS DECOMPOSABLE PROPOSITIONS TRUTH- TREE DEEOMPOSITION RULES 130 131 132 133 135 138 138 141 142 142 145 147 148 150 151 157 158 159 160 160 S PROPOSITIONAL LOGIE DERIVATIONS 5.1 PROOF CONSTRUETION 5.2 PREMISES AND THE GOAL PROPOSITION 5.3 INTELIM DERIVATION RULES 5.3.1 CONJUNETION INTRODUETION (AI) 5.3.2 CONJUNETION ELIMINATION (AE) EXEREISE SET # I SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET # I 5.3.3 ASSUMPTIONS (A) AND SUBPROOFS 5.3.4 CONDITIONALLNTRODUETION (--?I) 5.3.5 CONDITIONAL ELIMINATION (--?E) 5.3.6 REITERATION (R) EXERCISE SET #2 SOLUTIONS TO STARRED EXEREISES IN EXERCISE SET #2 5.3.7 NEGATION INTRODUETION (-,1) AND ELIMINATION (-,E) EXERCISE SET #3 SOLUTIONS TO STARRED EXERCISES IN EXEREISE SET #3 161 161 163 163 163 166 168 168 169 174 176 177 180 180 181 182 182 IMAGE 5 EXLENDED TABLE OJCONLENIS XIII 5.3.8 DISJUNETION INTRODUETION (VI) 184 5.3.9 DISJUNETION ELIMINATION (VE) 185 5.3.10 BIEONDITIONAL ELIMINATION AND LNTRODUETION (HE AND HI) 187 EXERCISE SET #4 189 SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET #4 191 5.4 STRATEGIES FOR PROOFS 194 5.4.1 STRATEGIES INVOLVING PREMISES 194 EXEREISE SET #5 198 SOLUTIONS TO STARRED EXEREISES IN EXEREISE SET #5 198 5.4.2 STRATEGIES INVOLVING ASSUMPTIONS 199 EXERCISE SET #6 206 SOLUTIONS TO STARRED EXERCISES IN EXEREISE SET #6 207 5.5 ADDITIONAL DERIVATION RULES (PD+) 209 5.5.1 DISJUNETIVE SYLLOGISM (DS) 209 5.5.2 MODUS TOLLENS (MT) 211 5.5.3 HYPOTHETIEAL SYLLOGISM (HS) 211 5.5.4 DOUBLE NEGATION (DN) 212 5.5.5 DE MORGAN S LAWS (DEM) 213 5.5.6 IMPLIEATION (LMP) 214 5.6 ADDITIONAL DERIVATION STRATEGIES 216 5.6.1 SAMPIE PROBLEM 219 END-OF-CHAPTER EXERCISES 223 EASY PROOFS 223 SOLUTIONS TO STARRED EASY PROOFS 224 MEDIUM PROOFS 226 SOLUTIONS TO STARRED MEDIUM PROOFS 227 HARD PROOFS 23 I SOLUTIONS TO STARRED HARD PROOFS 232 ZERO-PREMISE DEDUETIONS 236 SOLUTIONS TO STARRED ZERO-PREMISE DEDUETIONS 237 CONEEPTUAL AND APPLIEATION EXERCISES 240 LIST OF STRATEGIE RULES 241 STEP-BY-STEP USE OF STRATEGIE RULES FOR ASSUMPTIONS 242 LIST OF DERIVATION RULES FOR PD+ 242 DEFINITION 245 6 PREDIEATE LANGUAGE, SYNTAX, AND SEMANTIES 247 6.1 THE EXPRESSIVE POWER OF PREDICATE LOGIE 247 6.2 THE LANGUAGE OF RL 248 IMAGE 6 XIV EXTENDED TABLE OFCONTENTS 6.2.1 INDIVIDUAL CONSTANTS (NAMES) AND N-PLACE PREDICATES 248 6.2.2 DOMAIN OF DISCOURSE, INDIVIDUAL VARIABLES, AND QUANTIFIERS 251 6.2.3 PARENTHESES AND SCOPE OF QUANTIFIERS 253 EXERCISE SET # I 255 SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET # I 256 6.3 THE SYNTAX OF RL 256 6.3.1 FREE AND BOUND VARIABLES 256 6.3.2 MAIN OPERATOR IN PREDICATE WFFS 257 6.3.3 THE FORMAL SYNTAX OF RL: FORMATION RULES 258 EXERCISE SET #2 261 SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET #2 262 6.4 PREDICATE SEMANTICS 263 6.4.1 A LITTLE SET THEORY 263 6.4.2 PREDICATE SEMANTICS 264 EXERCISE SET #3 269 SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET #3 270 6.5 TRANSLATION FROM ENGLISH TO PREDICATE LOGIC 270 6.5.1 TRANSLATION KEYS 270 6.5.2 THE UNIVERSAL QUANTIFIER ( V ) 271 6.5.3 THE EXISTENTIAL QUANTIFIER (3) 273 6.5.4 TRANSLATION WALK THROUGH 275 6.5.5 SAM PIE TRANSLATIONS 276 EXERCISE SET #4 276 SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET #4 277 6.6 MIXED AND OVERLAPPING QUANTIFIERS 277 EXERCISE SET #5 280 SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET #5 281 DEFINITIONS 281 7 PREDICATE LOGIC TREES 283 7.1 FOUR NEW DECOMPOSITION RULES 283 7.2 STRATEGIES FOR DECOMPOSING TREES 291 EXERCISE SET # I 292 SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET # I 292 7.3 LOGICAL PROPERTIES 294 7.3.1 SEMANTIC ANALYSIS OF PREDICATE TRUTH TREES 296 7.3.2 CONSISTENCY AND INCONSISTENCY 299 IMAGE 7 EXLENDED TAB/E OJCONLENLS EXEREISE SET #2 SOLUTIONS TO STARRED EXEREISES IN EXERCISE SET #2 7.3.3 TAUTOLOGY, CONTRADIETION, AND CONTINGENEY EXEREISE SET #3 SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET #3 7.3.4 LOGICAL EQUIVALENEE EXERCISE SET #4 SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET #4 7.3.5 VALIDITY EXERCISE SET #5 SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET #5 7.4 UNDECIDABILITY AND THE LIMITS OFTHE PREDICATE TREE METHOD END-OF-CHAPTER EXEREISES SOLUTIONS TO STARRED EXERCISES IN END-OF-CHAPTER EXERCISES DEFINITIONS AND TREE RULES 8 PREDIEATE LOGIE DERIVATIONS 8.1 FOUR QUANTIFIER RULES 8.1.1 UNIVERSAL ELIMINATION ( TE) 8.1.2 EXISTENTIAL INTRODUETION (31) EXEREISE SET # I SOLUTIONS TO STARRED EXERCISES IN EXERCISE SET # I 8.1.3 UNIVERSALLNTRODUETION ( TL) 8.1.4 EXISTENTIAL ELIMINATION (3E) EXEREISE SET #2 SOLUTIONS TO STARRED EXEREISES IN EXERCISE SET #2 8.2 QUANTIFIER NEGATION (QN) 8.3 SAMPIE PROOFS END-OF-CHAPTER EXERCISES SOLUTIONS TO END-OF-CHAPTER EXERCISES SUMMARY OF DERIVATION AND STRATEGIE RULES APPENDIX FURTHER READING INDEX ABOUT THE AUTHOR XV 302 302 305 307 308 310 311 311 314 316 316 317 320 320 323 325 325 325 329 333 333 335 342 346 347 348 350 352 353 357 359 367 371 375 PHILOSOPHY I LOGIC ... ι 4 David W. ■ Agier, provides visually convincing examples that illustrate the con¬ cepts of symbolic logic effectively, a feature not commonly found in similar textbooks. The abundance of sample symbolizations and proofs in this book makes it ideal for classroom use. — Masato Ishida, University of Hawaii Agler s Symbolic Logic Syntax, Semantics, and Proof is a remarkably clear and systematic introduction to first-order formal logic. Notably, Agler does an excellent job in showing why we use these particular rules through multiple examples and step-by-step explanations of how they develop from general considerations of meaning and truth. This method of building up to the rules of symbolic logic will be incredibly helpful in improving student understand¬ ing, since it presents the formalism as something to be understood, rather than simply memorized. —Daniel Brunson, Morgan State University Brimming with visual examples of concepts, derivation rules, and proof strate¬ gies, this introductory text is ideal for students with no previous experience in logic. Symbolic Logic: Syntax, Semantics, and Proof introduces students to the fundamental concepts, techniques, and topics involved in deductive reasoning. David W. Agler guides students through the basics of symbolic logic by explaining the essentials of two classical systems—propositional and predicate logic. Students will learn translation both from formal language into English and from English into formal language; how to use truth trees and truth tables to test propositions for logical properties; and how to construct and strategically use derivation rules in proofs. This text makes the often con¬ founding subject of symbolic logic more accessible with step-by-step example proofs, chapter glossaries of key terms, hundreds of homework problems and solutions for practice, and suggested further readings.
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spellingShingle	Agler, David W. Symbolic logic syntax, semantics, and proof aLogic, Modern aLogic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd
subject_GND	(DE-588)4037951-6
title	Symbolic logic syntax, semantics, and proof
title_auth	Symbolic logic syntax, semantics, and proof
title_exact_search	Symbolic logic syntax, semantics, and proof
title_full	Symbolic logic syntax, semantics, and proof David W. Agler
title_fullStr	Symbolic logic syntax, semantics, and proof David W. Agler
title_full_unstemmed	Symbolic logic syntax, semantics, and proof David W. Agler
title_short	Symbolic logic
title_sort	symbolic logic syntax semantics and proof
title_sub	syntax, semantics, and proof
topic	aLogic, Modern aLogic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd
topic_facet	aLogic, Modern aLogic, Symbolic and mathematical Mathematische Logik
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