Verfügbarkeit: Language, proof, and logic | Technische Universität München

Language, proof, and logic:

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Bibliographische Detailangaben
Beteiligte Personen:	Barker-Plummer, Dave (VerfasserIn), Barwise, Jon 1942-2000 (VerfasserIn), Etchemendy, John 1952- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Stanford, Calif. CSLI Publ. 2011
Ausgabe:	2. ed.
Schlagwörter:	Logic Sprache Beweis Logik CD-ROM Einführung
Links:	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
Beschreibung:	Rev. ed. of: Language, proof, and logic / Jon Barwise & John Etchemendy. -- Includes index.
Umfang:	XIII, 606 S. in Behältnis 1 CD-ROM (12 cm), 1 Manual (VII, 56 S.)
ISBN:	9781575866321 1575866323

Internformat

MARC


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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-
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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

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