Fibring logics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon
1999
|
| Schriftenreihe: | Oxford logic guides
38 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 475 S. |
| ISBN: | 0198503814 |
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Datensatz im Suchindex
| _version_ | 1804126747352891392 |
|---|---|
| adam_text | FIBRING LOGICS DOV M. GABBAY KING S COLLEGE, LONDON CLARENDON PRESS *
OXFORD 1999 CONTENTS 1 AN OVERVIEW OF FIB RED SEMANTICS AND THE
COMBINATION OF LOGICS 1 1.1 INTRODUCTION 1 1.1.1 COMBINING PURE LOGICAL
SYSTEMS 2 1.1.2 COMBINING META-LEVEL WITH THE OBJECT LEVEL 4 1.1.3
SELF-FIBRING OF PREDICATE LOGICS 4 1.1.4 TEMPORALISING A SYSTEM 5 1.1.5
MAKING YOUR LOGIC FUZZY 5 1.1.6 COMBINING PROOF SYSTEMS 6 1.2
THELDEAOFFIBRING 6, 1.2.1 APPRECIATION OF THE DIFFICULTIES INVOLVED IN
COMBIN- ING SYSTEMS 7 1.2.2 THE BASIC IDEA OF FIBRING 9 1.2.3 GENERAL
FIBRING 10 1.2.4 CASE STUDY: MODAL LOGIC FIBRING AND DOVETAILING 14
1.2.5 STEP BY STEP SCENARIO FOR FIBRING TWO LOGICS 17 2 LOGICS AND THEIR
SEMANTICS 18 2.1 FIBRING BASIC RELATIONAL SEMANTICS 18 2.2 FIBRING
PREFERENTIAL SEMANTICS 26 2.3 COMPLETENESS THEOREMS*A DISCUSSION 36 3
COMBINING MODAL LOGICS 39 3.1 INTRODUCING MODAL FIBRING 39 3.1.1 BASIC
DEFINITIONS AND EXAMPLES 42 3.1.2 WAYS OF COMBINING 48 3.2 FIBRING
MODALITIES 53 3.3 DOVETAILING MODAL LOGICS 64 3.4 FIBRING AND
DOVETAILING MODAL FRAGMENTS 70 3.5 DECIDABILITY 74 4 INTUITIONISTIC
MODAL LOGICS 76 4.1 INTRODUCTION 76 4.2 FIBRING MODALITY INTO
INTUITIONISTIC LOGIC 77 5 DISCUSSION AND COMPARISON WITH THE LITERATURE
91 5.1 INTUITIONISTIC MODAL LOGICS 91 5.2 MULTIMODAL LOGICS 110 6
INTRODUCING SELF-FIBRING 112 6.1 INTRODUCTION AND BACKGROUND 112 6.2
FREE LOGIC 115 CONTENTS 7 SELF-FIBRING OF PREDICATE LOGICS 7.1
SELF-FIBRED SEMANTICS FOR SUBSTITUTION 7.1.1 DISCUSSION OF OUR OPTIONS
7.1.2 BASIC SEMANTICS AND COMPLETENESS THEOREMS 7.1.3 REFINEMENTS OF THE
SEMANTIC S 7.2 SELF-FIBRING AND EQUALITY 7.3 FIBRING PREDICATE LOGICS
WITH BINARY RELATIONS 8 SELF-FIBRING WITH FUNCTION SYMBOLS 8.1 FIBRING
PREDICATE LOGICS WITH FUNCTION SYMBOLS 8.2 FIBRED SEMANTICS FOR
AMBIVALENT SYNTAX 9 SELF-FIBRING OF INTUITIONISTIC LOGIC 9.1
INTRODUCTION 9.2 INTUITIONISTIC LANGUAGE WITH UNARY PREDICATES 9.3
INTUITIONISTIC LANGUAGE WITH BINARY PREDICATES 9.4 INTUITIONISTIC
LANGUAGE WITH UNARY FUNCTIONS 9.5 INTUITIONISTIC LANGUAGE WITH EQUALITY
9.6 FIBRING KRIPKE INTUITIONISTIC MODELS 10 APPLICATIONS OF SELF-FIBRING
10.1 CONNECTION AND TRANSLATION 10.2 FIXED POINT SELF-REFERENCE 10.3
NEMETI S GENERALISED ASSIGNMENT MODELS 10.4 GENERALISED QUANTIFIERS 10.5
MCCARTHY S AND BUVAC S CONTEXT SYSTEMS 10.5.1 THE SYSTEM B OF CONTEXT
10.5.2. COMPARISON WITH THE LITERATURE 10.6 NATURAL LANGUAGE QUANTIFIERS
10.6.1 INTRODUCTION 10.6.2 DYNAMIC TREATMENT OF QUANTIFIERS 10.6.3
CONCLUSION AND FURTHER APPLICATIONS 10.7 DEFAULT AND NON-MONOTONIC
REASONING 10.7.1 INTRODUCTION 10.7.2 THE OPERATOR M 10.7.3 THE
NON-MONOTONIC COMPONENT 10.7.4 RESTRICTED MONOTONICITY 10.7.5 CONNECTION
WITH FIBRING 10.8 THE SUBJUNCTIVE CONDITIONAL 10.9 DISCUSSION AND
CONCLUSION 11 CONDITIONAL IMPLICATIONS AND NON-MONOTONIC CONSEQUENCE
11.1 INTRODUCTION 11.2 NON-MONOTONIC COMPANION 11.3 REFLECTING INTO THE
OBJECT LEVEL 11.4 SEMANTICS FOR THE CONDITIONAL CONTENTS 12 HOW TO MAKE
YOUR LOGIC FUZZY 227 12.1 INTRODUCTION AND MOTIVATING EXAMPLES 227 12.2
FIBRING WITH LUKASIEWICZ LOGIC ... 231 12.3 FUZZY MODAL LOGIC 241 12.4
MAKING A FUZZY LOGIC EVEN MORE FUZZY 247 12.5 COMPARISON WITH THE
LITERATURE 251 12.6 CASE STUDY: FUZZY AUTOMATA 253 13 COMBINING TEMPORAL
LOGIC SYSTEMS 255 13.1 INTRODUCTION 255 13.2 PRELIMINARIES 260 13.3
COMBINING LOGICS 263 13.4 TEMPORALISING A LOGIC 266 13.5 INDEPENDENT
COMBINATION 268 13.6 FULL JOIN 272 13.7 RESTRICTED JOIN 274 13.8 THE
TWO-DIMENSIONAL DIAGONAL 277 13.9 CONCLUSION 281 14 FIBRING IMPLICATION
LOGICS 283 14.1 INTRODUCTION 283 14.2 BACKGROUND ON SUBSTRUCTURAL
IMPLICATION 284 14.2.1 CONSEQUENCE RELATIONS 284 14.2.2 UNIFORM
SEMANTICS FOR SUBSTRUCTURAL IMPLICATIONS 285 14.2.3 SOUNDNESS AND
COMPLETENESS 286 14.3 LKE 288 J4.3.1 THE CLASSICAL KE SYSTEM 289
14-3.2 LKE FOR SUBSTRUCTURAL IMPLICATION 289 14.4 FIBRING SUBSTRUCTURAL
IMPLICATION LOGICS 294 14.4.1 PRELIMINARY INVESTIGATIONS . 295 14.4.2
SIMPLIFIED FIBRED MODELS 298 14.4.3 STRUCTURED CONSEQUENCE RELATIONS 299
14.4.4 THE FIBRED CANONICAL MODEL 300 14.5 LKE FOR MULTI-IMPLICATION
SYSTEMS 301 14.5.1 EXAMPLES 302 15 GRAFTING MODALITIES ONTO
SUBSTRUCTURAL IMPLICATION SYSTEMS 307 15.1 INTRODUCTION 307 15.2
INFORMATION FRAMES 308 15.3 THE MODAL OPERATORS 309 SERIALITY 313
REFLEXIVITY 313 TRANSITIVITY 313 SYMMETRY 314 EUCLIDEANISM 314 CONTENTS
DIRECTEDNESS 15.4 THE CANONICAL MODEL 15.5 ADDING MODALITIES TO THE LKE
SYSTEM 15.5.1 MODAL LKE RULES ELIMINATION RULES FOR * ELIMINATION RULES
FOR O 15.5.2 SOME EXAMPLES 15.5.3 COMPLETENESS OF MODAL LKE 16 PRODUCTS
OF MODAL LOGICS 16.1 INTRODUCTION AND BACKGROUND 16.1.1 JOINING
(PRODUCT) OF KRIPKE SEMANTICS 16.1.2 FUSION OF TWO LOGICS 16.1.3
BACKGROUND RESULTS 16.2 BASIC DEFINITIONS AND NOTATIONS 16.3 FUSIONS AND
PRODUCTS 16.4 THICKENING AND UNRAVELLING 16.5 RECURSIVE AXIOMATISABILITY
16.6 PRODUCTS OF MINIMAL MODAL LOGICS 16.7 PRODUCTS OF PTC-LOGICS 16.8
COUNTEREXAMPLES 16.9 PRODUCTS OF SOME KNOWN SYSTEMS 16.9.1 THE LOGIC
S4.3 2 = S4.3 X S4.3 16.9.2 THE LOGIC S4.3 X S5 16.9.3 THE LOGICS S4.1.3
X S4.3,S4.1.3 2 ,S4.1.3 X S5 16.10 THE FINITE MODEL PROPERTY 16. IT
FINITE DEPTH AND MODEL PROPERTIES FOR K 2 16.12 TWO-DIMENSIONAL NORMAL
FORMS 16.13 THE FINITE MODEL PROPERTY VIA FILTRATIONS 16.14 APPLICATIONS
TO PREDICATE LOGICS ; : 16.15 CASE STUDY: TRANSITION SYSTEMS 16.16
CONCLUSION: FURTHER RESULTS AND QUESTIONS 17 FIBRING INTUITIONISTIC
LOGIC PROGRAMS 17.1 INTRODUCTION ^ 17.2 INTUITIONISTIC LOGIC PROGRAMMING
17.2.1 OVERVIEW 17.2.2 SYNTAX OF QN-PROLOG 17.2.3 PROCEDURAL SEMANTICS
OF QN-PROLOG 17.2.4 MODEL SEMANTICS OF QN-PROLOG 17.2.5 THE RELATION
BETWEEN PROCEDURAL AND MODEL SEMAN- TICS 17.2.6 AN EXAMPLE: SEMANTIC
TABLEAUX 17.3 FIBRING OF QN-PROLOG PROGRAMS 17.3.1 THE INTUITION BEHIND
FIBRING QN-PROLOG PROGRAMS CONTENTS 17.3.2 FIBRING PROCEDURAL SEMANTICS
391 17.3.3 FIBRING MODEL SEMANTICS 393 17.3.4 THE RELATION BETWEEN
FIBRED PROCEDURAL AND FIBRED MODEL SEMANTICS 395 17.3.5 FIBRING SEMANTIC
TABLEAUX AND RIGID ^-UNIFICATION 395 17.3.6 INSTANTIATING THE GENERAL
FRAMEWORK 397 17.4 INCREMENTAL DATABASES 399 17.5 CONCLUSION 400 18
FIBRING SEMANTIC TABLEAUX 401 18.1 INTRODUCTION 401 18.2 LOGICS 402 18.3
TABLEAU CALCULI 403 18.4 FIBRING OF LOGICS 409 18.5 EXAMPLE: FIRST-ORDER
PREDICATE LOGIC 410 18.5.1 THE LOGICAL SYSTEM OF FIRST-ORDER LOGIC 410
18.5.2 A TABLEAU CALCULUS FOR FIRST-ORDER LOGIC 411 18.6 FIBRING OF
TABLEAU CALCULI 416 18.6.1 EXAMPLE: FIBRING CALCULI FOR INTUITIONISTIC
LOGICS 417 19 FIBRING MODAL TABLEAUX 421 19.1 INTRODUCTION 421 19.2
LABEL FORMALISM 424 19.3 UNIFICATIONS 427 19.3.1 BASIC UNIFICATIONS
(AXIOM UNIFICATIONS) 427 19.3.2 HIGH UNIFICATIONS (COMBINED
UNIFICATIONS) 429 19.3.3 LOW UNIFICATION (LOGIC UNIFICATIONS) * 429
19.3.4.FIBRED UNIFICATION 430 19.4 INFERENCE RULES 432 19.5 SOUNDNESS
AND COMPLETENESS 434 20 FIBRING LABELLED DEDUCTIVE SYSTEMS 440 20.1
INTRODUCTION 440 20.2 VIEWING LDS AS A FIBRED LOGIC 444 20.3 FIBRING TWO
ALGEBRAS 445 21 CONCLUSION AND DISCUSSION 457 REFERENCES 459 INDEX 473
|
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| author | Gabbay, Dov M. 1945- |
| author_GND | (DE-588)124196314 |
| author_facet | Gabbay, Dov M. 1945- |
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| callnumber-raw | QA9 |
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| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012138293 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:22:22Z |
| institution | BVB |
| isbn | 0198503814 |
| language | English |
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| oclc_num | 40756941 |
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| physical | XIII, 475 S. |
| publishDate | 1999 |
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| publisher | Clarendon |
| record_format | marc |
| series | Oxford logic guides |
| series2 | Oxford logic guides |
| spelling | Gabbay, Dov M. 1945- Verfasser (DE-588)124196314 aut Fibring logics Dov. M. Gabbay Oxford Clarendon 1999 XIII, 475 S. txt rdacontent n rdamedia nc rdacarrier Oxford logic guides 38 Combinatorische logica gtt Logique floue ram Logique symbolique et mathématique ram Mathématiques intuitionnistes ram Modalité (logique) ram Programmation (mathématiques) ram logique floue inriac logique intuitionniste inriac logique modale inriac logique temporelle inriac sémantique inriac Logic, Symbolic and mathematical Logik (DE-588)4036202-4 gnd rswk-swf Faserung Mathematik (DE-588)4472884-0 gnd rswk-swf Logik (DE-588)4036202-4 s Faserung Mathematik (DE-588)4472884-0 s DE-604 Oxford logic guides 38 (DE-604)BV000013997 38 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008221392&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gabbay, Dov M. 1945- Fibring logics Oxford logic guides Combinatorische logica gtt Logique floue ram Logique symbolique et mathématique ram Mathématiques intuitionnistes ram Modalité (logique) ram Programmation (mathématiques) ram logique floue inriac logique intuitionniste inriac logique modale inriac logique temporelle inriac sémantique inriac Logic, Symbolic and mathematical Logik (DE-588)4036202-4 gnd Faserung Mathematik (DE-588)4472884-0 gnd |
| subject_GND | (DE-588)4036202-4 (DE-588)4472884-0 |
| title | Fibring logics |
| title_auth | Fibring logics |
| title_exact_search | Fibring logics |
| title_full | Fibring logics Dov. M. Gabbay |
| title_fullStr | Fibring logics Dov. M. Gabbay |
| title_full_unstemmed | Fibring logics Dov. M. Gabbay |
| title_short | Fibring logics |
| title_sort | fibring logics |
| topic | Combinatorische logica gtt Logique floue ram Logique symbolique et mathématique ram Mathématiques intuitionnistes ram Modalité (logique) ram Programmation (mathématiques) ram logique floue inriac logique intuitionniste inriac logique modale inriac logique temporelle inriac sémantique inriac Logic, Symbolic and mathematical Logik (DE-588)4036202-4 gnd Faserung Mathematik (DE-588)4472884-0 gnd |
| topic_facet | Combinatorische logica Logique floue Logique symbolique et mathématique Mathématiques intuitionnistes Modalité (logique) Programmation (mathématiques) logique floue logique intuitionniste logique modale logique temporelle sémantique Logic, Symbolic and mathematical Logik Faserung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008221392&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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