Language, proof, and logic:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Stanford, Calif.
CSLI Publ.
2011
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Rev. ed. of: Language, proof, and logic / Jon Barwise & John Etchemendy. -- Includes index. |
| Physical Description: | XIII, 606 S. in Behältnis 1 CD-ROM (12 cm), 1 Manual (VII, 56 S.) |
| ISBN: | 9781575866321 1575866323 |
Staff View
MARC
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| 245 | 1 | 0 | |a Language, proof, and logic |c Dave Barker-Plummer, Jon Barwise & John Etchemendy in collaboration with Albert Liu, Michael Murray, Emma Pease |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Stanford, Calif. |b CSLI Publ. |c 2011 | |
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Record in the Search Index
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| adam_text | IMAGE 1
ACKNOWLEDGEMENTS
INTRODUCTION THE SPECIAL ROLE OF LOGIC IN RATIONAL INQUIRY WHY LEARN AN
ARTIFICIALLANGUAGE? .
CONSEQUENCE AND PROOF. . . . . . . . . . . .
INSTRUCTIONS ABOUT HOMEWORK EXERCISES (ESSENTIAL!) TO THE INSTRUCTOR WEB
ADDRESS
I PROPOSITIONAL LOGIC
V
1
1 2 4 5
11 16
CONTENTS
1 ATOMIC SENTENCES 19
1.1 INDIVIDUAL CONSTANTS 19
1.2 PREDICATE SYMBOLS 20
1.3 ATOMIC SENTENCES . . 23
1.4 GENERAL FIRST-ORDER LANGUAGES 28
1.5 FUNCTION SYMBOLS (OPTIONAL) 31
1.6 THE FIRST-ORDER LANGUAGE OF SET THEORY (OPTIONAL) 37
1.7 THE FIRST-ORDER LANGUAGE OF ARITHMETIE (OPTIONAL) 38
1.8 ALTERNATIVE NOTATION (OPTIONAL) .......... 40
2 THE LOGIC OF ATOMIC SENTENCES 41
2.1 VALID AND SOUND ARGUMENTS 41
2.2 METHODS OF PROOF . . . . . . . 46
2.3 FORMAL PROOFS. . . . . . . . . 54
2.4 CONSTRUCTING PROOFS IN FITCH 58
2.5 DEMONSTRATING NONEONSEQUENCE . 63
2.6 ALTERNATIVE NOTATION (OPTIONAL) 66
3 THE BOOLEAN CONNECTIVES 67
3.1 NEGATION SYMBOL: --, .. 68
3.2 CONJUNCTION SYMBOL: 1 71
3.3 DISJUNCTION SYMBOL: V . 74
3.4 REMARKS ABOUT THE GAME 77
IX
IMAGE 2
X / CONTENTS
3.5 AMBIGUITY AND PARENTHESES . . .
3.6 EQUIVALENT WAYS OF SAYING THINGS 3.7 TRANSLATION...........
3.8 ALTERNATIVE NOTATION (OPTIONAL) .
79 82 84 90
CONTENTS
4 THE LOGIC OF BOOLEAN CONNECTIVES 93
4.1 TAUTOLOGIES AND LOGICAL TRUTH . . . 94
4.2 LOGICAL AND TAUTOLOGICAL EQUIVALENCE . 106
4.3 LOGICAL AND TAUTOLOGICAL CONSEQUENCE . 110
4.4 TAUTOLOGICAL CONSEQUENCE IN FITEH .. 114
4.5 PUSHING NEGATION AROUND (OPTIONAL) . 118
4.6 CONJUNCTIVE AND DISJUNCTIVE NORMAL FORMS (OPTIONAL) . 122
5 METHODS OF PROOF FOR BOOLEAN LOGIC 128
5.1 VALID INFERENEE STEPS . . . . . . . . . 129
5.2 PROOF BY EASES . . . . . . . . . . . . 132
5.3 INDIRECT PROOF: PROOF BY EONTRADIETION 137
5.4 ARGUMENTS WITH INEONSISTENT PREMISES (OPTIONAL) 141
6 FORMAL PROOFS AND BOOLEAN LOGIC 143
6.1 CONJUNCTION RULES 144
6.2 DISJUNETION RULES . . . . . . . 149
6.3 NEGATION RULES . . . . . . . . 156
6.4 THE PROPER USE OF SUBPROOFS . 165
6.5 STRATEGY AND TAETIES . . . . . 168
6.6 PROOFS WITHOUT PREMISES (OPTIONAL) 175
7 CONDITIONALS 178
7.1 MATERIAL EONDITIONAL SYMBOL: -+ 180
7.2 BIEONDITIONAL SYMBOL: F--T 183
7.3 CONVERSATIONAL IMPLIEATURE . . . 189
7.4 TRUTH-FUNETIONAL EOMPLETENESS (OPTIONAL) 192
7.5 ALTERNATIVE NOTATION (OPTIONAL) . . . . . . 198
8 THE LOGIC OF CONDITIONALS 199
8.1 INFORMAL METHODS OF PROOF. . . . . . . . 199
8.2 FORMAL RULES OF PROOF FOR -+ AND F--T . . . 207
8.3 SOUNDNESS AND EOMPLETENESS (OPTIONAL) 215
8.4 VALID ARGUMENTS: SOME REVIEW EXEREISES 223
IMAGE 3
11 QUANTIFIERS
9 INTRODUCTION TO QUANTIFICATION 9.1 VARIABLES AND ATOMIC WFFS ..
9.2 THE QUANTIFIER SYMBOLS: /,:3 .
9.3 WFFS AND SENTENCES .
9.4 SEMANTICS FOR THE QUANTIFIERS 9.5 THE FOUR ARISTOTELIAN FORMS .
9.6 TRANSLATING COMPLEX NOUN PHRASES 9.7 QUANTIFIERS AND FUNCTION
SYMBOLS (OPTIONAL) 9.8 ALTERNATIVE NOTATION (OPTIONAL) .
10 THE LOGIC OF QUANTIFIERS 10.1 TAUTOLOGIES AND QUANTIFICATION . . . .
. . . .
10.2 FIRST-ORDER VALIDITY AND CONSEQUENCE .....
10.3 FIRST-ORDER EQUIVALENCE AND DEMORGAN S LAWS 10.4 OTHER QUANTIFIER
EQUIVALENCES (OPTIONAL) 10.5 THE AXIOMATIC METHOD (OPTIONAL) .
10.6 LEMMAS .
11 MULTIPLE QUANTIFIERS 11.1 MULTIPLE USES OF A SINGLE QUANTIFIER 11.2
MIXED QUANTIFIERS .
11.3 THE STEP-BY-STEP METHOD OF TRANSLATION 11.4 PARAPHRASING
ENGLISHPARAPHRASING ENGLISH 11.5 AMBIGUITY AND CONTEXT SENSITIVITY .....
11.6 TRANSLATIONS USING FUNCTION SYMBOLS (OPTIONAL) 11. 7 PRENEX FORM
(OPTIONAL) .....
11.8 SOME EXTRA TRANSLATION PROBLEMS
12 METHODS OF PROOF FOR QUANTIFIERS 12.1 VALID QUANTIFIER STEPS .
12.2 THE METHOD OF EXISTENTIAL INSTANTIATION .
12.3 THE METHOD OF GENERAL CONDITIONAL PROOF.
12.4 PROOFS INVOLVING MIXED QUANTIFIERS 12.5 AXIOMATIZING SHAPE
(OPTIONAL)
13 FORMAL PROOFS AND QUANTIFIERS 13.1 UNIVERSAL QUANTIFIER RULES .
13.2 EXISTENTIAL QUANTIFIER RULES 13.3 STRATEGY AND TACTICS . . . .
229 230 232 233
237 241 245 253
257
259 259 267 277
282 286 291
298 298 302 307
309 313 317 320
324
328 328
331 332 338 347
351 351 356 361
CONTENTS / XI
CONTENTS
IMAGE 4
XII / CONTENTS
CONTENTS
13.4 SOUNDNESS AND COMPLETENESS (OPTIONAL)
13.5 SOME REVIEW EXERCISES (OPTIONAL) ..
14 MORE ABOUT QUANTIFIEATION (OPTIONAL) 14.1 NUMERICAL QUANTIFICATION
14.2 PROVING NUMERICAL CLAIMS .
14.3 THE, BOTH, AND NEITHER .
14.4 ADDING OTHER DETERMINERS TO FOL .
14.5 THE LOGIC OF GENERALIZED QUANTIFICATION
14.6 OTHER EXPRESSIVE LIMITATIONS OF FIRST-ORDER LOGIC
III APPLICATIONS AND METATHEORY
15 FIRST-ORDER SET THEORY 15.1 NAIVESETTHEORY .
15.2 THE EMPTY SET, SINGLETONS AND PAIRS 15.3 SUBSETS .
15.4 INTERSECTION AND UNION .
15.5 ORDERED PAIRS .
15.6 MODELING RELATIONS IN SET THEORY 15.7 FUNCTIONS .
15.8 THE POWERSET OF A SET (OPTIONAL) 15.9 RUSSELL S PARADOX (OPTIONAL)
15.10 ZERMELO FRANKEL SET THEORY (ZFC) (OPTIONAL)
16 MATHEMATIEAL INDUETION 16.1 INDUCTIVE DEFINITIONS AND INDUCTIVE
PROOFS 16.2 INDUCTIVE DEFINITIONS IN SET THEORY .
16.3 INDUCTION ON THE NATURAL NUMBERS .
16.4 AXIOMATIZING THE NATURAL NUMBERS (OPTIONAL) 16.5 INDUCTION IN FITEH
.
16.6 ORDERING THE NATURAL NUMBERS (OPTIONAL) 16.7 STRONG INDUETION
(OPTIONAL) .
17 ADVANEED TOPIES IN PROPOSITIONAL LOGIC
17.1 TRUTH ASSIGNMENTS AND TRUTH TABLES 17.2 COMPLETENESS FOR
PROPOSITIONALLOGIE 17.3 HORN SENTENCES (OPTIONAL) 17.4 RESOLUTION
(OPTIONAL) .
370 370
373 375 383
388 392 398 406
413 414 419 422
424 429 431 436
439 442 444
454 455 463
465 468 473 475
478
484 484 486 495
504
IMAGE 5
18 ADVANCED TOPICS IN FOL
18.1 FIRST-ORDER STRUCTURES .
18.2 TRUTH AND SATISFACTION, REVISITED 18.3 SOUNDNESS FAR FOL .
18.4 THE COMPLETENESS OF THE SHAPE AXIOMS (OPTIONAL)
18.5 SKOLEMIZATION (OPTIONAL) .... 18.6 UNIFICATION OF TERMS (OPTIONAL)
18.7 RESOLUTION, REVISITED (OPTIONAL)
19 COMPLETENESS AND INCOMPLETENESS 19.1 THE COMPLETENESS THEOREM FOR FOL
19.2 ADDING WITNESSING CONSTANTS
19.3 THE HENKIN THEORY .....
19.4 THE ELIMINATION THEOREM ..
19.5 THE HENKIN CONSTRUCTION ..
19.6 THE LWENHEIM-SKOLEM THEOREM.
19.7 THE COMPACTNESS THEOREM ....
19.8 THE GDEL INCOMPLETENESS THEOREM
SUMMARY OF FORMAL PROOF RULES PROPOSITIONAL RULES FIRST-ORDER RULES .
INDUCTION RULES . . . . . . . . . . .
INFERENCE PROCEDURES (CON RULES)
GLOSSARY
FILE INDEX
EXERCISE INDEX
GENERAL INDEX
511 511 516 525
528
530
532 535
542 543
545 547 550 556
562 564 568
573 573 575 577
577
579
590
593
595
CONTENTS / XIII
CONTENTS
|
| any_adam_object | 1 |
| author | Barker-Plummer, Dave Barwise, Jon 1942-2000 Etchemendy, John 1952- |
| author_GND | (DE-588)124163092 (DE-588)132926679 |
| author_facet | Barker-Plummer, Dave Barwise, Jon 1942-2000 Etchemendy, John 1952- |
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| building | Verbundindex |
| bvnumber | BV039685872 |
| callnumber-first | B - Philosophy, Psychology, Religion |
| callnumber-label | BC71 |
| callnumber-raw | BC71 |
| callnumber-search | BC71 |
| callnumber-sort | BC 271 |
| callnumber-subject | BC - Logic |
| classification_rvk | CC 2400 |
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| ctrlnum | (OCoLC)726620713 (DE-599)BVBBV039685872 |
| dewey-full | 160 |
| dewey-hundreds | 100 - Philosophy & psychology |
| dewey-ones | 160 - Philosophical logic |
| dewey-raw | 160 |
| dewey-search | 160 |
| dewey-sort | 3160 |
| dewey-tens | 160 - Philosophical logic |
| discipline | Informatik Philosophie |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV039685872 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:08:57Z |
| institution | BVB |
| isbn | 9781575866321 1575866323 |
| language | English |
| lccn | 2011019703 |
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| physical | XIII, 606 S. in Behältnis 1 CD-ROM (12 cm), 1 Manual (VII, 56 S.) |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | CSLI Publ. |
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| spelling | Barker-Plummer, Dave Verfasser aut Language, proof, and logic Dave Barker-Plummer, Jon Barwise & John Etchemendy in collaboration with Albert Liu, Michael Murray, Emma Pease 2. ed. Stanford, Calif. CSLI Publ. 2011 XIII, 606 S. in Behältnis 1 CD-ROM (12 cm), 1 Manual (VII, 56 S.) txt rdacontent n rdamedia nc rdacarrier Rev. ed. of: Language, proof, and logic / Jon Barwise & John Etchemendy. -- Includes index. Logic Sprache (DE-588)4056449-6 gnd rswk-swf Beweis (DE-588)4132532-1 gnd rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf CD-ROM (DE-588)4139307-7 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Logik (DE-588)4036202-4 s DE-604 Sprache (DE-588)4056449-6 s Beweis (DE-588)4132532-1 s CD-ROM (DE-588)4139307-7 s Barwise, Jon 1942-2000 Verfasser (DE-588)124163092 aut Etchemendy, John 1952- Verfasser (DE-588)132926679 aut V:DE-604 application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024534778&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barker-Plummer, Dave Barwise, Jon 1942-2000 Etchemendy, John 1952- Language, proof, and logic Logic Sprache (DE-588)4056449-6 gnd Beweis (DE-588)4132532-1 gnd Logik (DE-588)4036202-4 gnd CD-ROM (DE-588)4139307-7 gnd |
| subject_GND | (DE-588)4056449-6 (DE-588)4132532-1 (DE-588)4036202-4 (DE-588)4139307-7 (DE-588)4151278-9 |
| title | Language, proof, and logic |
| title_auth | Language, proof, and logic |
| title_exact_search | Language, proof, and logic |
| title_full | Language, proof, and logic Dave Barker-Plummer, Jon Barwise & John Etchemendy in collaboration with Albert Liu, Michael Murray, Emma Pease |
| title_fullStr | Language, proof, and logic Dave Barker-Plummer, Jon Barwise & John Etchemendy in collaboration with Albert Liu, Michael Murray, Emma Pease |
| title_full_unstemmed | Language, proof, and logic Dave Barker-Plummer, Jon Barwise & John Etchemendy in collaboration with Albert Liu, Michael Murray, Emma Pease |
| title_short | Language, proof, and logic |
| title_sort | language proof and logic |
| topic | Logic Sprache (DE-588)4056449-6 gnd Beweis (DE-588)4132532-1 gnd Logik (DE-588)4036202-4 gnd CD-ROM (DE-588)4139307-7 gnd |
| topic_facet | Logic Sprache Beweis Logik CD-ROM Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024534778&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT barkerplummerdave languageproofandlogic AT barwisejon languageproofandlogic AT etchemendyjohn languageproofandlogic |