Holdings: Truth and falsehood

Truth and falsehood: an inquiry into generalized logical values

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Bibliographic Details
Main Authors:	Šramko, Jaroslav Vladyslavovyč 1963- (Author), Wansing, Heinrich (Author)
Format:	Book
Language:	English
Published:	Dordrecht [u.a.] Springer 2011
Series:	Trends in logic 36
Subjects:	Intuitionistische Logik Mathematische Logik
Online Access:	Inhaltsverzeichnis
Physical Description:	XIII, 246 S. graph. Darst.
ISBN:	9789400709065

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adam_text	IMAGE 1 CONTENTS 1 TRUTH VALUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 THE IDEA OF TRUTH VALUES . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 TRUTH VALUES AND THE FUNCTIONAL ANALYSIS OF LANGUAGE. . . . . . 3 1.3 THE CATEGORIAL STATUS OF TRUTH AND FALSEHOOD . . . . . . . . . . . . 5 1.4 THE ONTOLOGICAL BACKGROUND OF TRUTH VALUES . . . . . . . . . . . . 7 1.5 LOGIC AS THE SCIENCE OF LOGICAL VALUES. . . . . . . . . . . . . . . . . 10 1.6 LOGICAL STRUCTURES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.7 TRUTH VALUES, TRUTH DEGREES, AND VAGUE CONCEPTS. . . . . . . . . 15 2 TRUTH VALUES AND THE SLINGSHOT ARGUMENT. . . . . . . . . . . . . . . . . . 19 2.1 AN ARGUMENT IN FAVOR OF TRUTH VALUES .. . . . . . . . . . . . . . . 19 2.2 RECONSTRUCTING THE SLINGSHOT ARGUMENTS . . . . . . . . . . . . . . . . 20 2.2.1 CHURCH S SLINGSHOT. . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2.2 GDEL S SLINGSHOT. . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2.3 DAVIDSON S SLINGSHOT . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3 THE SLINGSHOT ARGUMENT AND NON-FREGEAN LOGIC. . . . . . . . . . 25 2.4 NON-FREGEAN LOGIC AND DEFINITE DESCRIPTIONS . . . . . . . . . . . . 29 2.5 NON-FREGEAN LOGIC AND A-EXPRESSIONS . . . . . . . . . . . . . . . . . 34 2.6 NON-FREGEAN LOGIC AND INDEFINITE DESCRIPTIONS . . . . . . . . . . . 37 2.7 CONCLUDING REMARKS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3 GENERALIZED TRUTH VALUES: FROM FOUR Z TO SIXTEEN 3. . . . . . . . 41 3.1 TRUTH VALUES AS STRUCTURED ENTITIES. . . . . . . . . . . . . . . . . . . . 41 3.2 GENERALIZED VALUATIONS, FOUR-VALUED LOGIC AND BILATTICES. . . . 44 3.3 TAKING GENERALIZATION SERIOUSLY: FROM ISOLATED COMPUTERS TO COMPUTER NETWORKS . . . . . . . . . . . . . . . . . . . . 48 3.4 GENERALIZED TRUTH VALUES AND MULTILATTICES . . . . . . . . . . . . . . 51 3.5 THE TRILATTICE OF 16 TRUTH VALUES. . . . . . . . . . . . . . . . . . . . . 53 3.6 ANOTHER EXAMPLE OF A TRILATTICE: TRUTH VALUES IN CONSTRUCTIVE LOGICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 XL IMAGE 2 XLI CONTENTS 4 GENERALIZED TRUTH VALUES: SIXTEEN 3 AND BEYOND . . . . . . . . . . . 63 4.1 ENTAILMENT RELATIONS ON SIXTEEN 3. . . * * * * . * . . . . . . * * . . . 63 4.2 FIRST-DEGREE SYSTEMS FOR SIXTEEN 3 . * * * * * * . . . . . . * * * . . * 65 4.2.1 THE LANGUAGES SET,SE! AND SYSTEMS FDE;, FDEJ. . . . 65 4.2.2 THE LANGUAGE SE TF FOR::::: T AND:::::! . . . . . . . . . . . . . . . . 69 4.3 FIRST-DEGREE EVERYWHERE. . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.4 HYPER-CONTRADICTIONS AND GENERALIZATIONS OF PRIEST S LOGIC. . . 79 4.5 AN APPROACH TO A GENERALIZATION OF KLEENE S LOGIC: A TETRALATTICE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.6 UNCERTAINTY VERSUS LACK OF INFORMATION. . . . . . . . . . . . . . . . 89 5 AXIOM SYSTEMS FOR TRILATTICE LOGICS . . . . . . . . . . . . . . . . . . . . . . 93 5.1 TRUTH VALUE LATTICES AND THE IMPLICATION CONNECTIVE . . . . . . . 93 5.2 FROM FIRST-DEGREE PROOF SYSTEMS TO PROOF SYSTEMS WITH MODUS PONENS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.3 ODINTSOV S AXIOMATIZATION OF TRUTH ENTAILMENT AND FALSITY ENTAILMENT IN SIXTEEN 3. . . . . . . . * * . * . . . . . . * * * . 96 5.3.1 FIRST-DEGREE CALCULI . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.3.2 SYSTEMS WITH MODUS PONENS AS THE SOLE RULE OF INFERENCE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 106 5.4 DISCUSSION..................................... 110 6 SEQUENT SYSTEMS FOR TRILATTICE LOGICS . . . . . . . . . . . . . . . . . . . .. 113 6.1 STANDARD SEQUENT SYSTEMS FOR LOGICS RELATED TO SIXTEEN 3 * * . . . . . * * * * * . . . . . . . . . * * * . . . . . . . . . ** 114 6.2 ALTERNATIVE SEQUENT CALCULI . . . . . . . . . . . . . . . . . . . . . . . .. 122 6.3 EXTENSIONS..................................... 127 6.4 SEQUENT CALCULI FOR TRUTH ENTAILMENT AND FALSITY ENTAILMENT IN SIXTEEN 3 . * * . * . . . . . . . . . * * . . . . . . . . * ** 132 7 INTUITIONISTIC TRILATTICE LOGICS. . . . . . . . . . . . . . . . . . . . . . . . . .. 143 7.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 143 7.2 SEQUENT CALCULUS 1 16. . * * . . . . . . . . . . * * . . . . . . . . . * * * .. 145 7.3 KRIPKE COMPLETENESS FOR 1 16 * * . . . . . . * * * . * . . . . . . . * * .* 155 7.4 TABLEAU CALCULUS IT 16. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 160 7.5 KRIPKE COMPLETENESS FOR IT I6 . . . . . . . . . . . . . . . . . . . . . .. 164 8 GENERALIZED TRUTH VALUES AND MANY-VALUED LOGICS: HARMONIOUS MANY-VALUED LOGICS 171 8.1 MANY- VALUED PROPOSITIONAL LOGICS GENERALIZED . . . . . . . . . .. 171 8.2 DESIGNATED AND ANTIDESIGNATED VALUES . . . . . . . . . . . . . . . .. 175 8.3 SOME SEPARATED FINITELY-VALUED LOGICS . . . . . . . . . . . . . . .. 178 8.4 A HARMONIOUS LOGIC INSPIRED BY THE LOGIC OF SIXTEEN 3. . .. 181 IMAGE 3 CONTENTS X11I 8.5 HARMONY AD INFINITUM. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 182 8.6 SOME REMARKS ON GENERALIZING HARMONY . . . . . . . . . . . . . .. 183 9 GENERALIZED TRUTH VALUES AND MANY-VALUED LOGICS: SUSZKO S THESIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 189 9.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 189 9.2 THE SUSZKO REDUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 192 9.2.1 MALINOWSKI S ANALYSIS OF SUSZKO S THESIS. . . . . . . .. 195 9.2.2 TSUJI S ANALYSIS OF SUSZKO S THESIS. . . . . . . . . . . . .. 197 9.3 LOGICAL N-VALUEDNESS AS INFERENTIAL MANY-VALUEDNESS . . . . .. 198 9.3.1 WHAT IS A LOGICAL VALUE? . . . . . . . . . . . . . . . . . . . .. 198 9.3.2 ANOTHER KIND OF COUNTEREXAMPLE. . . . . . . . . . . . . . .. 201 9.3.3 EXAMPLES OF NATURAL BI-CONSEQUENCE LOGICS. . . . . . .. 202 9.3.4 LOGICALLY N-VALUED LOGICS 203 9.4 ANOTHER ANALYSIS AND A RESUME. . . . . . . . . . . . . . . . . . . . .. 206 9.5 A BILATTICE OF FOUR ENTAILMENT RELATIONS. . . . . . . . . . . . . . .. 207 9.5.1 DEFINITIONS OF FOUR ENTAILMENT RELATIONS . . . . . . . . .. 208 9.5.2 ORDERINGS ON ENTAILMENT RELATIONS. . . . . . . . . . . . . .. 211 9.5.3 CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . .. 213 10 FURTHER DEVELOPMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 215 10.1 FIRST-ORDER TRILATTICE LOGICS 215 10.2 MODAL TRILATTICE LOGICS. . . . . . . . . . . . . . . . . . . . . . . . . . .. 217 10.3 ADVERBIALLY QUALIFIED TROTH VALUES . . . . . . . . . . . . . . . . . .. 220 10.4 GENERALIZED TROTH VALUES: ALTERNATE INTERPRETATIONS. . . . . . .. 222 REFERENCES 227 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 239
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author	Šramko, Jaroslav Vladyslavovyč 1963- Wansing, Heinrich
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spelling	Šramko, Jaroslav Vladyslavovyč 1963- Verfasser (DE-588)1056097825 aut Truth and falsehood an inquiry into generalized logical values Yaroslav Shramko, Heinrich Wansing Dordrecht [u.a.] Springer 2011 XIII, 246 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Trends in logic 36 Intuitionistische Logik (DE-588)4162199-2 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Intuitionistische Logik (DE-588)4162199-2 s DE-604 Mathematische Logik (DE-588)4037951-6 s Wansing, Heinrich Verfasser aut Trends in logic 36 (DE-604)BV011512969 36 V:DE-604 application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024594117&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Šramko, Jaroslav Vladyslavovyč 1963- Wansing, Heinrich Truth and falsehood an inquiry into generalized logical values Trends in logic Intuitionistische Logik (DE-588)4162199-2 gnd Mathematische Logik (DE-588)4037951-6 gnd
subject_GND	(DE-588)4162199-2 (DE-588)4037951-6
title	Truth and falsehood an inquiry into generalized logical values
title_auth	Truth and falsehood an inquiry into generalized logical values
title_exact_search	Truth and falsehood an inquiry into generalized logical values
title_full	Truth and falsehood an inquiry into generalized logical values Yaroslav Shramko, Heinrich Wansing
title_fullStr	Truth and falsehood an inquiry into generalized logical values Yaroslav Shramko, Heinrich Wansing
title_full_unstemmed	Truth and falsehood an inquiry into generalized logical values Yaroslav Shramko, Heinrich Wansing
title_short	Truth and falsehood
title_sort	truth and falsehood an inquiry into generalized logical values
title_sub	an inquiry into generalized logical values
topic	Intuitionistische Logik (DE-588)4162199-2 gnd Mathematische Logik (DE-588)4037951-6 gnd
topic_facet	Intuitionistische Logik Mathematische Logik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024594117&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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