Symbolic logic: syntax, semantics, and proof
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Lanham, Md. [u.a.]
Rowman & Littlefield Publishers
2013
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Includes bibliographical references (p. ) and index |
| Beschreibung: | XIX, 375 S. |
| ISBN: | 9781442217423 9781442217416 |
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| 300 | |a XIX, 375 S. | ||
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Datensatz im Suchindex
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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.
|
| any_adam_object | 1 |
| author | Agler, David W. |
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| building | Verbundindex |
| bvnumber | BV040770120 |
| callnumber-first | B - Philosophy, Psychology, Religion |
| callnumber-label | BC38 |
| callnumber-raw | BC38 |
| callnumber-search | BC38 |
| callnumber-sort | BC 238 |
| callnumber-subject | BC - Logic |
| classification_rvk | CC 2600 SK 130 |
| ctrlnum | (OCoLC)828810509 (DE-599)GBV721182518 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| format | Book |
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| id | DE-604.BV040770120 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:33:33Z |
| institution | BVB |
| isbn | 9781442217423 9781442217416 |
| language | English |
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| publishDate | 2013 |
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| publisher | Rowman & Littlefield Publishers |
| record_format | marc |
| spelling | Agler, David W. Verfasser (DE-588)1031573259 aut Symbolic logic syntax, semantics, and proof David W. Agler Lanham, Md. [u.a.] Rowman & Littlefield Publishers 2013 XIX, 375 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. ) and index aLogic, Modern aLogic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 Erscheint auch als Online-Ausgabe 978-1-442-21743-0 Digitalisierung UB Erlangen application/pdf 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 Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf 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 Klappentext |
| 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 |
| url | 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 |
| work_keys_str_mv | AT aglerdavidw symboliclogicsyntaxsemanticsandproof |