Hybrid logic and its proof-theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Roskilde
Roskilde University, Dept. of Communication, Business and Information
2009
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 318 S. |
Staff View
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| adam_text | CONTENTS PREFACE 1 INTRODUCTION TO HYBRID LOGIC 1.1 INFORMAL MOTIVATION
. . .. .. 1.2 FORMAL SYNTAX AND SEMANTICS ... 1.2.1 TRANSLATION INTO
FIRST-ORDER LOGIC 1.3 THE ORIGIN OF HYBRID LOGIC IN PRIOR S WORK 1.3.1
DID PRIOR REACH HIS PHILOSOPHICAL GOAL? 1.4 THE DEVELOPMENT SINCE PRIOR
. . 2 PROOF-THEORY OF PROPOSITIONAL HYBRID LOGIC 2.1 THE BASICS OF
NATURAL DEDUCTION SYSTEMS 2.2 NATURAL DEDUCTION FOR PROPOSITION AL
HYBRID LOGIC 2.2.1 CONDITIONS ON THE ACCESSIBILITY RELATION 2.2.2 SOME
ADMISSIBLE MIES ... 2.2.3 SOUNDNESS AND COMPLETENESS . 2.2.4
NORMALIZATION. . ... 2.2.5 THE FORM OF NORMAL DERIVATIONS 2.2.6
DISCUSSION. . . 2.3 THE BASICS OF GENTZEN SYSTEMS .. 2.4 GENTZEN SYSTEMS
FOR PROPOSITIONAL HYBRID LOGIC 2.4.1 SOUNDNESS AND COMPLETENESS 2.4.2
THE FORM OF DERIVATIONS . 2.4.3 DISCUSSION. .. 2.5 AXIOM SYSTEMS FOR
PROPOSITIONAL HYBRID LOGIC 2.5.1 SOUNDNESS AND COMPLETENESS 2.5.2
DISCUSSION. . . .. .. 3 TABLEAUS AND DECISION PROCEDURES FOR HYBRID
LOGIC 3.1 THE BASICS OF TABLEAU SYSTEMS . .. .. 3.2 A TABLEAU SYSTEM
INCLUDING THE UNIVERSAL MODALITY . 3 7 13 13 17 20 23 28 30 35 35 39 43
46 47 52 59 62 64 66 68 69 70 70 72 74 75 75 78 4 3.2.1 TABLEAU RULES
FOR HYBRID LOGIC ..... 3.2.2 SOME PROPERTIES OF THE TABLEAU SYSTEM 3.2.3
SYSTEMATIC TABLEAU CONSTRUCTION . . . . 3.2.4 THE MODEL EXISTENCE
THEOREM AND DECIDABILITY 3.2.5 TABLEAU EXAMPLES . . . . . . . . . . . .
. . . . 3.3 A TABLEAU SYSTEM NOT INCLUDING THE UNIVERSAL MODALITY 3.3.1
A HYBRID-IOGICAL VERSION OF ANALYTIC CUTS .... 3.4 THE TABLEAU SYSTEMS
REFORMULATED AS GENTZEN SYSTEMS . 3.5
DISCUSSION......................... 4 COMPARISON TO SELIGMAN S NATURAL
DEDUCTION SYSTEM 4.1 THE NATURAL DEDUCTION SYSTEMS UNDER CONSIDERATION
4.1.1 SELIGMAN S ORIGINAL SYSTEM . 4.2 TRANSLATION FROM SELIGMAN-STYLE
DERIVATIONS . 4.3 TRANSLATION TO SELIGMAN-STYLE DERIVATIONS 4.4
REDUCTION RULES 4.5 DISCUSSION................. 5 FUNCTIONAL
COMPLETENESS FOR TWO HYBRID LOGICS 5.1 THE NATURAL DEDUCTION SYSTEMS
UNDER CONSIDERATION 5.2 INTRODUCTION TO FUNCTIONAL COMPLETENESS . 5.3
THE GENERAL RULE SCHEMAS . 5.3.1 EARLIER WORK ON FUNCTIONAL COMPLETENESS
5.3.2 RULE SCHEMAS FOR HYBRID LOGIC . . . . . . 5.3.3 NORMALIZATION AND
CONSERVATIVITY .... 5.4 FUNCTIONAL COMPLETENESS WITH THE UNIVERSAL
MODALITY 5.5 FUNCTIONAL COMPLETENESS WITH THE DIFFERENCE MODALITY 5.6
DISCUSSION . 6 FIRST-ORDER HYBRID LOGIC 6.1 INTRODUCTION TO FIRST-ORDER
HYBRID LOGIC . 6.1.1 SOME REMARKS ON EXISTENCE AND QUANTIFICATION 6.1.2
RIGIDIFIED CONSTANTS . 6.1.3 TRANSLATION INTO TWO-SORTED FIRST-ORDER
LOGIC . 6.2 NATURAL DEDUCTION FOR FIRST-ORDER HYBRID LOGIC . 6.2.1
CONDITIONS ON THE ACCESSIBILITY RELATION 6.2.2 SOME ADMISSIBLE RULES ...
6.2.3 SOUNDNESS AND COMPLETENESS .. 6.2.4 NORMALIZATION . 6.2.5 THE FORM
OF NORMAL DERIVATIONS 6.3 AXIOM SYSTEMS FOR FIRST-ORDER HYBRID LOGIC
CONTENTS 78 80 83 84 88 93 97 100 106 111 111 114 115 118 122 127 129
129 133 134 135 138 141 143 147 152 155 155 159 161 163 167 170 172 172
177 179 181 CONTENTS 7 INTENSIONAL FIRST-ORDER HYBRID LOGIC 7.1
INTRODUCTION TO INTENSIONAL FIRST-ORDER HYBRID LOGIC 7.1.1 GENERALIZED
MODELS . 7.1. 2 TRANSLATION INTO THREE-SORTED FIRST-ORDER LOGIC 7.2 NAT
URAL DEDUCTION FOR INTENSIONAL FIRST-ORDER HYBRID LOGIC 7.2.1 SOUNDNESS
AND COMPLETENESS: GENERALIZED MODELS 7.2.2 SOUNDNESS AND COMPLETENESS:
STANDARD MODELS. 7.3 PARTIAL INTENSIONS . 8 INTUITIONISTIC HYBRID LOGIC
8.1 INTRODUCTION TO INTUITIONISTIC HYBRID LOGIC . 8.1.1 TRANSLATION INTO
INTUITIONISTIC FIRST-ORDER LOGIC 8.2 NATURAL DEDUCTION FOR
INTUITIONISTIC HYBRID LOGIC 8.2.1 CONDITIONS ON THE ACCESSIBILITY
RELATION 8.2.2 AN ADMISSIBLE RULE . . . . . 8.2.3 SOUNDNESS AND
COMPLETENESS . . 8.2.4 NORMALIZATION . 8.2.5 THE FORM OF NORMAL
DERIVATIONS 8.3 AXIOM SYSTEMS FOR INTUITIONISTIC HYBRID LOGIC 8.4 AXIOM
SYSTEMS FOR A PARACONSISTENT HYBRID LOGIC 8.4.1 SOUNDNESS AND
COMPLETENESS ..... 9 WHY DOES THE PROOF-THEORY WORK SO WEIL? 9.1
LABELLED VERSUS INTERNALIZED NATURAL DED UCTION 9.1.1 THE
INTERNALIZATION TRANSLATION . 9.1.2 REDUCTIONS . 9.1.3 COMPARISON OF
REDUCTIONS . 9.1.4 MORE ON NORMALIZATION ... 9.2 WHY THE PROOF-THEORY
WORKS SO WEH 9.2.1 STANDARD SYSTEMS FOR MODALLOGIC 9.2.2 LABEHED SYSTEMS
FOR MODALLOGIC 9.2.3 INTERNALIZED SYSTEMS FOR HYBRID LOGIC 9.2.4
COMPARISON TO INTERNALIZATION OF BIVALENT SEMANTICS 9.3 SOME CONCLUDING
PHILOSOPHICAL REMARKS . A MODAL LOGIC, TRUTH, AND THE MASTER MODALITY
A.L INTRODUCTION. . . . . . . . . . . . . . . . . . . . A.2 MODALLOGIC
AND TRUTH . A.2.1 PROPOSITIONAL AND FIRST-ORDER MODALLOGIC A.2.2
DAVIDSON S NOTION OF A THEORY OF TRUTH A.2.3 THEORIES OF TRUTH FOR
MODALLOGIC .... 5 185 185 190 192 196 197 199 201 203 203 208 210 210
213 213 217 222 224 226 229 233 233 235 235 237 239 241 242 243 244 247
249 251 251 254 254 255 257 6 A.3 THEORIES OF TRUTH AND THE MASTER
MODALITY A.3.1 THE MASTER MODALITY . A.3.2 THE CONDITION OF
N-BOUNDEDNESS . . A.3.3 EXAMPLES . . . . . . . . . . . . . . AA THE
UNIVERSAL MODALITY, THE MASTER MODALITY, HYBRID LOGIC . AA.I HYBRID
MODALLOGIC . AA.2 THE UNIVERSAL MODALITY AND HYBRID LOGIC AA.3 THE
MASTER MODALITY AND HYBRID LOGIC . AAA PRIOR S FOURTH GRADE TENSE LOGIC
..... B A CUT-FREE GENTZEN FORMULATION OF 55 B.I INTRODUCTION .. B.2
DEFINITION OF 55 B.3 THE EQUIVALENCE BA CUT-ELIMINATION BA.I A
PRELIMINARY RESULT BA.2 THE KEY-CASES . . . . BA.3 PUTTING THE PROOF
TOGETHER B.5 RELATED WORK ON MODAL LOGIC . DANSK SAMMENFATNING
BIBLIOGRAPHY INDEX CONTENTS 259 259 262 264 265 265 267 269 273 215 275
277 280 284 284 285 286 289 293 291 315
|
| adam_txt |
CONTENTS PREFACE 1 INTRODUCTION TO HYBRID LOGIC 1.1 INFORMAL MOTIVATION
. . . . 1.2 FORMAL SYNTAX AND SEMANTICS . 1.2.1 TRANSLATION INTO
FIRST-ORDER LOGIC 1.3 THE ORIGIN OF HYBRID LOGIC IN PRIOR'S WORK 1.3.1
DID PRIOR REACH HIS PHILOSOPHICAL GOAL? 1.4 THE DEVELOPMENT SINCE PRIOR
. . 2 PROOF-THEORY OF PROPOSITIONAL HYBRID LOGIC 2.1 THE BASICS OF
NATURAL DEDUCTION SYSTEMS 2.2 NATURAL DEDUCTION FOR PROPOSITION AL
HYBRID LOGIC 2.2.1 CONDITIONS ON THE ACCESSIBILITY RELATION 2.2.2 SOME
ADMISSIBLE MIES . 2.2.3 SOUNDNESS AND COMPLETENESS . 2.2.4
NORMALIZATION. . . 2.2.5 THE FORM OF NORMAL DERIVATIONS 2.2.6
DISCUSSION. . . 2.3 THE BASICS OF GENTZEN SYSTEMS . 2.4 GENTZEN SYSTEMS
FOR PROPOSITIONAL HYBRID LOGIC 2.4.1 SOUNDNESS AND COMPLETENESS 2.4.2
THE FORM OF DERIVATIONS . 2.4.3 DISCUSSION. . 2.5 AXIOM SYSTEMS FOR
PROPOSITIONAL HYBRID LOGIC 2.5.1 SOUNDNESS AND COMPLETENESS 2.5.2
DISCUSSION. . . . . 3 TABLEAUS AND DECISION PROCEDURES FOR HYBRID
LOGIC 3.1 THE BASICS OF TABLEAU SYSTEMS . . . 3.2 A TABLEAU SYSTEM
INCLUDING THE UNIVERSAL MODALITY . 3 7 13 13 17 20 23 28 30 35 35 39 43
46 47 52 59 62 64 66 68 69 70 70 72 74 75 75 78 4 3.2.1 TABLEAU RULES
FOR HYBRID LOGIC . 3.2.2 SOME PROPERTIES OF THE TABLEAU SYSTEM 3.2.3
SYSTEMATIC TABLEAU CONSTRUCTION . . . . 3.2.4 THE MODEL EXISTENCE
THEOREM AND DECIDABILITY 3.2.5 TABLEAU EXAMPLES . . . . . . . . . . . .
. . . . 3.3 A TABLEAU SYSTEM NOT INCLUDING THE UNIVERSAL MODALITY 3.3.1
A HYBRID-IOGICAL VERSION OF ANALYTIC CUTS . 3.4 THE TABLEAU SYSTEMS
REFORMULATED AS GENTZEN SYSTEMS . 3.5
DISCUSSION. 4 COMPARISON TO SELIGMAN'S NATURAL
DEDUCTION SYSTEM 4.1 THE NATURAL DEDUCTION SYSTEMS UNDER CONSIDERATION
4.1.1 SELIGMAN'S ORIGINAL SYSTEM . 4.2 TRANSLATION FROM SELIGMAN-STYLE
DERIVATIONS . 4.3 TRANSLATION TO SELIGMAN-STYLE DERIVATIONS 4.4
REDUCTION RULES 4.5 DISCUSSION. 5 FUNCTIONAL
COMPLETENESS FOR TWO HYBRID LOGICS 5.1 THE NATURAL DEDUCTION SYSTEMS
UNDER CONSIDERATION 5.2 INTRODUCTION TO FUNCTIONAL COMPLETENESS . 5.3
THE GENERAL RULE SCHEMAS . 5.3.1 EARLIER WORK ON FUNCTIONAL COMPLETENESS
5.3.2 RULE SCHEMAS FOR HYBRID LOGIC . . . . . . 5.3.3 NORMALIZATION AND
CONSERVATIVITY . 5.4 FUNCTIONAL COMPLETENESS WITH THE UNIVERSAL
MODALITY 5.5 FUNCTIONAL COMPLETENESS WITH THE DIFFERENCE MODALITY 5.6
DISCUSSION . 6 FIRST-ORDER HYBRID LOGIC 6.1 INTRODUCTION TO FIRST-ORDER
HYBRID LOGIC . 6.1.1 SOME REMARKS ON EXISTENCE AND QUANTIFICATION 6.1.2
RIGIDIFIED CONSTANTS . 6.1.3 TRANSLATION INTO TWO-SORTED FIRST-ORDER
LOGIC . 6.2 NATURAL DEDUCTION FOR FIRST-ORDER HYBRID LOGIC . 6.2.1
CONDITIONS ON THE ACCESSIBILITY RELATION 6.2.2 SOME ADMISSIBLE RULES .
6.2.3 SOUNDNESS AND COMPLETENESS . 6.2.4 NORMALIZATION . 6.2.5 THE FORM
OF NORMAL DERIVATIONS 6.3 AXIOM SYSTEMS FOR FIRST-ORDER HYBRID LOGIC
CONTENTS 78 80 83 84 88 93 97 100 106 111 111 114 115 118 122 127 129
129 133 134 135 138 141 143 147 152 155 155 159 161 163 167 170 172 172
177 179 181 CONTENTS 7 INTENSIONAL FIRST-ORDER HYBRID LOGIC 7.1
INTRODUCTION TO INTENSIONAL FIRST-ORDER HYBRID LOGIC 7.1.1 GENERALIZED
MODELS . 7.1. 2 TRANSLATION INTO THREE-SORTED FIRST-ORDER LOGIC 7.2 NAT
URAL DEDUCTION FOR INTENSIONAL FIRST-ORDER HYBRID LOGIC 7.2.1 SOUNDNESS
AND COMPLETENESS: GENERALIZED MODELS 7.2.2 SOUNDNESS AND COMPLETENESS:
STANDARD MODELS. 7.3 PARTIAL INTENSIONS . 8 INTUITIONISTIC HYBRID LOGIC
8.1 INTRODUCTION TO INTUITIONISTIC HYBRID LOGIC . 8.1.1 TRANSLATION INTO
INTUITIONISTIC FIRST-ORDER LOGIC 8.2 NATURAL DEDUCTION FOR
INTUITIONISTIC HYBRID LOGIC 8.2.1 CONDITIONS ON THE ACCESSIBILITY
RELATION 8.2.2 AN ADMISSIBLE RULE . . . . . 8.2.3 SOUNDNESS AND
COMPLETENESS . . 8.2.4 NORMALIZATION . 8.2.5 THE FORM OF NORMAL
DERIVATIONS 8.3 AXIOM SYSTEMS FOR INTUITIONISTIC HYBRID LOGIC 8.4 AXIOM
SYSTEMS FOR A PARACONSISTENT HYBRID LOGIC 8.4.1 SOUNDNESS AND
COMPLETENESS . 9 WHY DOES THE PROOF-THEORY WORK SO WEIL? 9.1
LABELLED VERSUS INTERNALIZED NATURAL DED UCTION 9.1.1 THE
INTERNALIZATION TRANSLATION . 9.1.2 REDUCTIONS . 9.1.3 COMPARISON OF
REDUCTIONS . 9.1.4 MORE ON NORMALIZATION . 9.2 WHY THE PROOF-THEORY
WORKS SO WEH 9.2.1 STANDARD SYSTEMS FOR MODALLOGIC 9.2.2 LABEHED SYSTEMS
FOR MODALLOGIC 9.2.3 INTERNALIZED SYSTEMS FOR HYBRID LOGIC 9.2.4
COMPARISON TO INTERNALIZATION OF BIVALENT SEMANTICS 9.3 SOME CONCLUDING
PHILOSOPHICAL REMARKS . A MODAL LOGIC, TRUTH, AND THE MASTER MODALITY
A.L INTRODUCTION. . . . . . . . . . . . . . . . . . . . A.2 MODALLOGIC
AND TRUTH . A.2.1 PROPOSITIONAL AND FIRST-ORDER MODALLOGIC A.2.2
DAVIDSON'S NOTION OF A THEORY OF TRUTH A.2.3 THEORIES OF TRUTH FOR
MODALLOGIC . 5 185 185 190 192 196 197 199 201 203 203 208 210 210
213 213 217 222 224 226 229 233 233 235 235 237 239 241 242 243 244 247
249 251 251 254 254 255 257 6 A.3 THEORIES OF TRUTH AND THE MASTER
MODALITY A.3.1 THE MASTER MODALITY . A.3.2 THE CONDITION OF
N-BOUNDEDNESS . . A.3.3 EXAMPLES . . . . . . . . . . . . . . AA THE
UNIVERSAL MODALITY, THE MASTER MODALITY, HYBRID LOGIC . AA.I HYBRID
MODALLOGIC . AA.2 THE UNIVERSAL MODALITY AND HYBRID LOGIC AA.3 THE
MASTER MODALITY AND HYBRID LOGIC . AAA PRIOR'S FOURTH GRADE TENSE LOGIC
. B A CUT-FREE GENTZEN FORMULATION OF 55 B.I INTRODUCTION . B.2
DEFINITION OF 55 B.3 THE EQUIVALENCE BA CUT-ELIMINATION BA.I A
PRELIMINARY RESULT BA.2 THE KEY-CASES . . . . BA.3 PUTTING THE PROOF
TOGETHER B.5 RELATED WORK ON MODAL LOGIC . DANSK SAMMENFATNING
BIBLIOGRAPHY INDEX CONTENTS 259 259 262 264 265 265 267 269 273 215 275
277 280 284 284 285 286 289 293 291 315 |
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| index_date | 2024-07-02T21:41:15Z |
| indexdate | 2024-07-09T21:19:57Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016672720 |
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| physical | 318 S. |
| publishDate | 2009 |
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| publisher | Roskilde University, Dept. of Communication, Business and Information |
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| spelling | Braüner, Torben Verfasser aut Hybrid logic and its proof-theory Torben Braüner Roskilde Roskilde University, Dept. of Communication, Business and Information 2009 318 S. txt rdacontent n rdamedia nc rdacarrier Zugl.: Roskilde, Univ., Diss., 2009 Hybrid logik Beweistheorie (DE-588)4145177-6 gnd rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Logik (DE-588)4036202-4 s Beweistheorie (DE-588)4145177-6 s DE-604 Digitalisierung UB Erlangen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016672720&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Braüner, Torben Hybrid logic and its proof-theory Hybrid logik Beweistheorie (DE-588)4145177-6 gnd Logik (DE-588)4036202-4 gnd |
| subject_GND | (DE-588)4145177-6 (DE-588)4036202-4 (DE-588)4113937-9 |
| title | Hybrid logic and its proof-theory |
| title_auth | Hybrid logic and its proof-theory |
| title_exact_search | Hybrid logic and its proof-theory |
| title_exact_search_txtP | Hybrid logic and its proof-theory |
| title_full | Hybrid logic and its proof-theory Torben Braüner |
| title_fullStr | Hybrid logic and its proof-theory Torben Braüner |
| title_full_unstemmed | Hybrid logic and its proof-theory Torben Braüner |
| title_short | Hybrid logic and its proof-theory |
| title_sort | hybrid logic and its proof theory |
| topic | Hybrid logik Beweistheorie (DE-588)4145177-6 gnd Logik (DE-588)4036202-4 gnd |
| topic_facet | Hybrid logik Beweistheorie Logik Hochschulschrift |
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