Classical and nonclassical logics: an introduction to the mathematics of propositions
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton [u.a.]
Princeton University Press
2005
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | IX, 507 S. |
| ISBN: | 0691122792 9780691122793 |
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Datensatz im Suchindex
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| adam_text | CLASSICAL AND NONCLASSICAL LOGICS AN INTRODUCTION TO THE MATHEMATICS OF
PROPOSITIONS ERIC SCHECHTER PRINCETON UNIVERSITY PRESS PRINCETON AND
OXFORD CONTENTS A PRELIMINARIES 1 1 INTRODUCTION FOR TEACHERS 3 *
PURPOSE AND INTENDED AUDIENCE, 3 * TOPICS IN THE BOOK, 6 * WHY
PLURALISM?, 13 * FEEDBACK, 18 * ACKNOWLEDGMENTS, 19 2 INTRODUCTION FOR
STUDENTS 20 * WHO SHOULD STUDY LOGIC?, 20 * FORMALISM AND CERTIFI-
CATION, 25 * LANGUAGE AND LEVELS, 34 * SEMANTICS AND SYNTACTICS, 39 *
HISTORICAL PERSPECTIVE, 49 * PLURALISM, 57 * JARDEN S EXAMPLE
(OPTIONAL), 63 3 INFORMAL SET THEORY 65 * SETS AND THEIR MEMBERS, 68 *
RUSSELL S PARADOX, 77 * SUBSETS, 79 * FUNCTIONS, 84 * THE AXIOM OF
CHOICE (OPTIONAL), 92 * OPERATIONS ON SETS, 94 * VENN DIA- GRAMS, 102 *
SYLLOGISMS (OPTIONAL), 111 * INFINITE SETS (POSTPONABLE), 116 4
TOPOLOGIES AND INTERIORS (POSTPONABLE) 126 * TOPOLOGIES, 127 *
INTERIORS, 133 * GENERATED TOPOLOGIES AND FINITE TOPOLOGIES (OPTIONAL),
139 5 ENGLISH AND INFORMAL CLASSICAL LOGIC 146 * LANGUAGE AND BIAS, 146
* PARTS OF SPEECH, 150 * SEMANTIC VALUES, 151 * DISJUNCTION (OR), 152 *
CON- JUNCTION (AND), 155 * NEGATION (NOT), 156 * MATERIAL IMPLICATION,
161 * COTENABILITY, FUSION, AND CONSTANTS VI CONTENTS (POSTPONABLE), 170
* METHODS OF PROOF, 174 * WORKING BACKWARDS, 177 * QUANTIFIERS, 183 *
INDUCTION, 195 * INDUCTION EXAMPLES (OPTIONAL), 199 6 DEFINITION OF A
FORMAL LANGUAGE 206 * THE ALPHABET, 206 * THE GRAMMAR, 210 * REMOVING
PARENTHESES, 215 * DENNED SYMBOLS, 219 * PREFIX NOTATION (OPTIONAL), 220
* VARIABLE SHARING, 221 * FORMULA SCHEMES, 222 * ORDER PRESERVING OR
REVERSING SUBFORMULAS (POSTPONABLE), 228 B SEMANTICS 233 7 DEFINITIONS
FOR SEMANTICS 235 * INTERPRETATIONS, 235 * FUNCTIONAL INTERPRETATIONS,
237 * TAUTOLOGY AND TRUTH PRESERVATION, 240 8 NUMERICALLY VALUED
INTERPRETATIONS 245 * THE TWO-VALUED INTERPRETATION, 245 * FUZZY
INTERPRE- TATIONS, 251 * TWO INTEGER-VALUED INTERPRETATIONS, 258 * MORE
ABOUT COMPARATIVE LOGIC, 262 * MORE ABOUT SUGIHARA S INTERPRETATION, 263
9 SET-VALUED INTERPRETATIONS 269 * POWERSET INTERPRETATIONS, 269 *
HEXAGON INTERPRETATION (OPTIONAL), 272 * THE CRYSTAL INTERPRETATION, 273
* CHURCH S DIAMOND (OPTIONAL), 277 10 TOPOLOGICAL SEMANTICS
(POSTPONABLE) 281 * TOPOLOGICAL INTERPRETATIONS, 281 * EXAMPLES, 282 *
COMMON TAUTOLOGIES, 285 * NONREDUNDANCY OF SYM- BOLS, 286 * VARIABLE
SHARING, 289 * ADEQUACY OF FINITE TOPOLOGIES (OPTIONAL), 290 *
DISJUNCTION PROPERTY (OP- TIONAL), 293 CONTENTS VII 11 MORE ADVANCED
TOPICS IN SEMANTICS 295 * COMMON TAUTOLOGIES, 295 * IMAGES OF
INTERPRETA- TIONS, 301 * DUGUNDJI FORMULAS, 307 C BASIC SYNTACTICS 311
12 INFERENCE SYSTEMS 313 13 BASIC IMPLICATION 318 * ASSUMPTIONS OF BASIC
IMPLICATION, 319 * A FEW EASY DERIVATIONS, 320 * LEMMALESS EXPANSIONS,
326 * DE- TACHMENTAL COROLLARIES, 330 * ITERATED IMPLICATION (POST-
PONABLE), 332 14 BASIC LOGIC 336 * FURTHER ASSUMPTIONS, 336 * BASIC
POSITIVE LOGIC, 339 * BASIC NEGATION, 341 * SUBSTITUTION PRINCIPLES, 343
D ONE-FORMULA EXTENSIONS 349 15 CONTRACTION 351 * WEAK CONTRACTION, 351
* CONTRACTION, 355 16 EXPANSION AND POSITIVE PARADOX 357 * EXPANSION AND
MINGLE, 357 * POSITIVE PARADOX (STRONG EXPANSION), 359 * FURTHER
CONSEQUENCES OF POSITIVE PARA- DOX, 362 17 EXPLOSION 365 18 FUSION 369
19 NOT-ELIMINATION 372 * NOT-ELIMINATION AND CONTRAPOSITIVES, 372 *
INTERCHANGE- ABILITY RESULTS, 373 * MISCELLANEOUS CONSEQUENCES OF NOT-
ELIMINATION, 375 VIII CONTENTS 20 RELATIVITY 377 E SOUNDNESS AND MAJOR
LOGICS 381 21 SOUNDNESS 383 22 CONSTRUCTIVE AXIOMS: AVOIDING
NOT-ELIMINATION 385 * CONSTRUCTIVE IMPLICATION, 386 * HERBRAND-TARSKI
DE- DUCTION PRINCIPLE, 387 * BASIC LOGIC REVISITED, 393 * SOUNDNESS, 397
* NONCONSTRUCTIVE AXIOMS AND CLASSICAL LOGIC, 399 * GLIVENKO S
PRINCIPLE, 402 23 RELEVANT AXIOMS: AVOIDING EXPANSION 405 * SOME
SYNTACTIC RESULTS, 405 * RELEVANT DEDUCTION PRINCIPLE (OPTIONAL), 407 *
SOUNDNESS, 408 * MINGLE: SLIGHTLY IRRELEVANT, 411 * POSITIVE PARADOX AND
CLASSICAL LOGIC, 415 24 FUZZY AXIOMS: AVOIDING CONTRACTION 417 * AXIOMS,
417 * MEREDITH S CHAIN PROOF, 419 * ADDI- TIONAL NOTATIONS, 421 *
WAJSBERG LOGIC, 422 * DEDUCTION PRINCIPLE FOR WAJSBERG LOGIC, 426 25
CLASSICAL LOGIC 430 * AXIOMS, 430 * SOUNDNESS RESULTS, 431 *
INDEPENDENCE OF AXIOMS, 431 26 ABELIAN LOGIC 437 F ADVANCED RESULTS 441
27 HARROP S PRINCIPLE FOR CONSTRUCTIVE LOGIC 443 * MEYER S VALUATION,
443 * HARROP S PRINCIPLE, 448 * THE DISJUNCTION PROPERTY, 451 *
ADMISSIBILITY, 451 * RESULTS IN OTHER LOGICS, 452
|
| adam_txt |
CLASSICAL AND NONCLASSICAL LOGICS AN INTRODUCTION TO THE MATHEMATICS OF
PROPOSITIONS ERIC SCHECHTER PRINCETON UNIVERSITY PRESS PRINCETON AND
OXFORD CONTENTS A PRELIMINARIES 1 1 INTRODUCTION FOR TEACHERS 3 *
PURPOSE AND INTENDED AUDIENCE, 3 * TOPICS IN THE BOOK, 6 * WHY
PLURALISM?, 13 * FEEDBACK, 18 * ACKNOWLEDGMENTS, 19 2 INTRODUCTION FOR
STUDENTS 20 * WHO SHOULD STUDY LOGIC?, 20 * FORMALISM AND CERTIFI-
CATION, 25 * LANGUAGE AND LEVELS, 34 * SEMANTICS AND SYNTACTICS, 39 *
HISTORICAL PERSPECTIVE, 49 * PLURALISM, 57 * JARDEN'S EXAMPLE
(OPTIONAL), 63 3 INFORMAL SET THEORY 65 * SETS AND THEIR MEMBERS, 68 *
RUSSELL'S PARADOX, 77 * SUBSETS, 79 * FUNCTIONS, 84 * THE AXIOM OF
CHOICE (OPTIONAL), 92 * OPERATIONS ON SETS, 94 * VENN DIA- GRAMS, 102 *
SYLLOGISMS (OPTIONAL), 111 * INFINITE SETS (POSTPONABLE), 116 4
TOPOLOGIES AND INTERIORS (POSTPONABLE) 126 * TOPOLOGIES, 127 *
INTERIORS, 133 * GENERATED TOPOLOGIES AND FINITE TOPOLOGIES (OPTIONAL),
139 5 ENGLISH AND INFORMAL CLASSICAL LOGIC 146 * LANGUAGE AND BIAS, 146
* PARTS OF SPEECH, 150 * SEMANTIC VALUES, 151 * DISJUNCTION (OR), 152 *
CON- JUNCTION (AND), 155 * NEGATION (NOT), 156 * MATERIAL IMPLICATION,
161 * COTENABILITY, FUSION, AND CONSTANTS VI CONTENTS (POSTPONABLE), 170
* METHODS OF PROOF, 174 * WORKING BACKWARDS, 177 * QUANTIFIERS, 183 *
INDUCTION, 195 * INDUCTION EXAMPLES (OPTIONAL), 199 6 DEFINITION OF A
FORMAL LANGUAGE 206 * THE ALPHABET, 206 * THE GRAMMAR, 210 * REMOVING
PARENTHESES, 215 * DENNED SYMBOLS, 219 * PREFIX NOTATION (OPTIONAL), 220
* VARIABLE SHARING, 221 * FORMULA SCHEMES, 222 * ORDER PRESERVING OR
REVERSING SUBFORMULAS (POSTPONABLE), 228 B SEMANTICS 233 7 DEFINITIONS
FOR SEMANTICS 235 * INTERPRETATIONS, 235 * FUNCTIONAL INTERPRETATIONS,
237 * TAUTOLOGY AND TRUTH PRESERVATION, 240 8 NUMERICALLY VALUED
INTERPRETATIONS 245 * THE TWO-VALUED INTERPRETATION, 245 * FUZZY
INTERPRE- TATIONS, 251 * TWO INTEGER-VALUED INTERPRETATIONS, 258 * MORE
ABOUT COMPARATIVE LOGIC, 262 * MORE ABOUT SUGIHARA'S INTERPRETATION, 263
9 SET-VALUED INTERPRETATIONS 269 * POWERSET INTERPRETATIONS, 269 *
HEXAGON INTERPRETATION (OPTIONAL), 272 * THE CRYSTAL INTERPRETATION, 273
* CHURCH'S DIAMOND (OPTIONAL), 277 10 TOPOLOGICAL SEMANTICS
(POSTPONABLE) 281 * TOPOLOGICAL INTERPRETATIONS, 281 * EXAMPLES, 282 *
COMMON TAUTOLOGIES, 285 * NONREDUNDANCY OF SYM- BOLS, 286 * VARIABLE
SHARING, 289 * ADEQUACY OF FINITE TOPOLOGIES (OPTIONAL), 290 *
DISJUNCTION PROPERTY (OP- TIONAL), 293 CONTENTS VII 11 MORE ADVANCED
TOPICS IN SEMANTICS 295 * COMMON TAUTOLOGIES, 295 * IMAGES OF
INTERPRETA- TIONS, 301 * DUGUNDJI FORMULAS, 307 C BASIC SYNTACTICS 311
12 INFERENCE SYSTEMS 313 13 BASIC IMPLICATION 318 * ASSUMPTIONS OF BASIC
IMPLICATION, 319 * A FEW EASY DERIVATIONS, 320 * LEMMALESS EXPANSIONS,
326 * DE- TACHMENTAL COROLLARIES, 330 * ITERATED IMPLICATION (POST-
PONABLE), 332 14 BASIC LOGIC 336 * FURTHER ASSUMPTIONS, 336 * BASIC
POSITIVE LOGIC, 339 * BASIC NEGATION, 341 * SUBSTITUTION PRINCIPLES, 343
D ONE-FORMULA EXTENSIONS 349 15 CONTRACTION 351 * WEAK CONTRACTION, 351
* CONTRACTION, 355 16 EXPANSION AND POSITIVE PARADOX 357 * EXPANSION AND
MINGLE, 357 * POSITIVE PARADOX (STRONG EXPANSION), 359 * FURTHER
CONSEQUENCES OF POSITIVE PARA- DOX, 362 17 EXPLOSION 365 18 FUSION 369
19 NOT-ELIMINATION 372 * NOT-ELIMINATION AND CONTRAPOSITIVES, 372 *
INTERCHANGE- ABILITY RESULTS, 373 * MISCELLANEOUS CONSEQUENCES OF NOT-
ELIMINATION, 375 VIII CONTENTS 20 RELATIVITY 377 E SOUNDNESS AND MAJOR
LOGICS 381 21 SOUNDNESS 383 22 CONSTRUCTIVE AXIOMS: AVOIDING
NOT-ELIMINATION 385 * CONSTRUCTIVE IMPLICATION, 386 * HERBRAND-TARSKI
DE- DUCTION PRINCIPLE, 387 * BASIC LOGIC REVISITED, 393 * SOUNDNESS, 397
* NONCONSTRUCTIVE AXIOMS AND CLASSICAL LOGIC, 399 * GLIVENKO'S
PRINCIPLE, 402 23 RELEVANT AXIOMS: AVOIDING EXPANSION 405 * SOME
SYNTACTIC RESULTS, 405 * RELEVANT DEDUCTION PRINCIPLE (OPTIONAL), 407 *
SOUNDNESS, 408 * MINGLE: SLIGHTLY IRRELEVANT, 411 * POSITIVE PARADOX AND
CLASSICAL LOGIC, 415 24 FUZZY AXIOMS: AVOIDING CONTRACTION 417 * AXIOMS,
417 * MEREDITH'S CHAIN PROOF, 419 * ADDI- TIONAL NOTATIONS, 421 *
WAJSBERG LOGIC, 422 * DEDUCTION PRINCIPLE FOR WAJSBERG LOGIC, 426 25
CLASSICAL LOGIC 430 * AXIOMS, 430 * SOUNDNESS RESULTS, 431 *
INDEPENDENCE OF AXIOMS, 431 26 ABELIAN LOGIC 437 F ADVANCED RESULTS 441
27 HARROP'S PRINCIPLE FOR CONSTRUCTIVE LOGIC 443 * MEYER'S VALUATION,
443 * HARROP'S PRINCIPLE, 448 * THE DISJUNCTION PROPERTY, 451 *
ADMISSIBILITY, 451 * RESULTS IN OTHER LOGICS, 452 |
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| language | English |
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| spelling | Schechter, Eric Verfasser aut Classical and nonclassical logics an introduction to the mathematics of propositions Eric Schechter Princeton [u.a.] Princeton University Press 2005 IX, 507 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Wiskundige logica gtt Mathematik Philosophie Mathematics Philosophy Proposition (Logic) Proposition (DE-588)4240283-9 gnd rswk-swf Nichtklassische Logik (DE-588)4197462-1 gnd rswk-swf Klassische Logik (DE-588)4333219-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Klassische Logik (DE-588)4333219-5 s Proposition (DE-588)4240283-9 s Nichtklassische Logik (DE-588)4197462-1 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014158628&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schechter, Eric Classical and nonclassical logics an introduction to the mathematics of propositions Wiskundige logica gtt Mathematik Philosophie Mathematics Philosophy Proposition (Logic) Proposition (DE-588)4240283-9 gnd Nichtklassische Logik (DE-588)4197462-1 gnd Klassische Logik (DE-588)4333219-5 gnd |
| subject_GND | (DE-588)4240283-9 (DE-588)4197462-1 (DE-588)4333219-5 (DE-588)4123623-3 |
| title | Classical and nonclassical logics an introduction to the mathematics of propositions |
| title_auth | Classical and nonclassical logics an introduction to the mathematics of propositions |
| title_exact_search | Classical and nonclassical logics an introduction to the mathematics of propositions |
| title_exact_search_txtP | Classical and nonclassical logics an introduction to the mathematics of propositions |
| title_full | Classical and nonclassical logics an introduction to the mathematics of propositions Eric Schechter |
| title_fullStr | Classical and nonclassical logics an introduction to the mathematics of propositions Eric Schechter |
| title_full_unstemmed | Classical and nonclassical logics an introduction to the mathematics of propositions Eric Schechter |
| title_short | Classical and nonclassical logics |
| title_sort | classical and nonclassical logics an introduction to the mathematics of propositions |
| title_sub | an introduction to the mathematics of propositions |
| topic | Wiskundige logica gtt Mathematik Philosophie Mathematics Philosophy Proposition (Logic) Proposition (DE-588)4240283-9 gnd Nichtklassische Logik (DE-588)4197462-1 gnd Klassische Logik (DE-588)4333219-5 gnd |
| topic_facet | Wiskundige logica Mathematik Philosophie Mathematics Philosophy Proposition (Logic) Proposition Nichtklassische Logik Klassische Logik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014158628&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schechtereric classicalandnonclassicallogicsanintroductiontothemathematicsofpropositions |