Multi dimensional modal logic:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1997
|
| Series: | Applied logic series
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 239 S. graph. Darst. |
| ISBN: | 079234345X |
Staff View
MARC
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Record in the Search Index
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| adam_text | MULTI-DIMENSIONAL MODAL LOGIC BY MAARTEN MARX DEPARTMENT OF COMPUTING,
IMPERIAL COLLEGE, LONDON, UNITED KINGDOM AND YDE VENEMA CIS, FREE
UNIVERSITY, AMSTERDAM, THE NETHERLANDS KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON CONTENTS PREFACE XIII 1 MULTI-DIMENSIONAL
MODAL LOGIC 1 1.1 WHAT IS MULTI-DIMENSIONAL MODAL LOGIC? 1 1.2
MANIFESTATIONS OF MULTI-DIMENSIONAL MODAL LOGICS 2 1.3 THEMES AND
QUESTIONS 6 1.4 OVERVIEW OF THE BOOK 8 1.5 HOW TO READ THIS BOOK 9 2
TWO-DIMENSIONAL MODAL LOGICS 11 2.1 OPERATIONS ON THE SQUARE UNIVERSE 11
2.2 AXIOMATIZING S5-SQUARE 13 2.3 CYLINDRIC MODAL LOGIC OF SQUARES 19
2.3.1 EXPRESSIVE POWER OF MLR2 20 2.3.2 TWO-DIMENSIONAL CORRESPONDENCE
21 2.3.3 TWO-DIMENSIONAL COMPLETENESS 23 2.4 THE MODAL LOGIC OF
COMPOSITION 26 2.4.1 COMPLETENESS AND INCOMPLETENESS 28 2.4.2
DECIDABILITY . . 30 2.5 A TWO-DIMENSIONAL TEMPORAL LOGIC 33 2.5.1
CHARACTERIZING THE TWO-DIMENSIONAL FRAMES 35 2.5.2 AXIOMATIZING THE
TWO-DIMENSIONAL FRAMES 38 2.6 HISTORICAL NOTES 41 3 ARROW LOGIC 43 3.1
INTRODUCTION 43 3.2 MOTIVATION 49 3.3 ARROW LOGIC AND RELATION ALGEBRAS
51 3.4 CONNECTION WITH FIRST ORDER LOGIC 56 3.5 CHARACTERIZING (LOCAL)
SQUARES 58 3.5.1 RA AXIOMS AS MODAL FORMULAS 59 3.5.2 FIRST-ORDER
CHARACTERIZATIONS 63 3.5.3 MODAL CHARACTERIZATIONS 65 3.6 AXIOMATIZING
(LOCAL) SQUARES 66 3.6.1 AXIOMATIZING SQUARES 66 3.6.2 AXIOMATIZING
LOCAL SQUARES 70 3.6.3 THE ALGEBRAIC SIDE . . . 73 IX 3.7 DECIDABILITY
AND INTERPOLATION 74 3.7.1 DECIDABILITY 74 3.7.2 INTERPOLATION 76 3.8
TEMPORAL ARROW LOGIC 78 3.8.1 DEFINITIONS 78 3.8.2 EXPRESSIVENESS 80
3.8.3 AXIOMATICS: THE GENERAL CASE 84 3.8.4 COMPLETENESS FOR
WELL-ORDERINGS 85 3.9 OTHER DIRECTIONS IN ARROW LOGIC 88 MODAL LOGICS OF
INTERVALS 93 4.1 INTRODUCTION 93 4.1.1 TIME IN PERIODS 93 4.1.2
INTERVALS AS TWO-DIMENSIONAL POINTS 96 4.2 THE SYSTEM HS: INTRODUCTION
97 4.3 THE SYSTEM HS: EXPRESSIVENESS 101 4.4 THE SYSTEM HS: AXIOMATICS
105 MODAL LOGICS OF RELATIONS 113 5.1 INTRODUCTION 113 5.2 MODALIZING
FIRST-ORDER LOGIC 115 5.3 ABSTRACT AND GENERALIZED ASSIGNMENT FRAMES 119
5.4 CHARACTERIZING CUBES AND LOCAL CUBES 124 5.4.1 CHARACTERIZING CUBES
FOR CML .*. . 124 5.4.2 CHARACTERIZING LOCAL CUBES FOR MLR 133 5.5
META-PROPERTIES 134 5.5.1 AXIOMATIZING CUBES FOR CML 135 5.5.2
AXIOMATIZING LOCAL CUBES FOR MLR 138 5.5.3 DECIDABILITY 146 5.5.4
INTERPOLATION 149 5.6 INFINITE DIMENSIONS 151 5.6.1 INFINITE-DIMENSIONAL
CYLINDRIC MODAL LOGIC 152 5.6.2 MODALIZING ORDINARY FIRST-ORDER LOGIC
154 5.6.3 W-DIMENSIONAL MODAL LOGIC 156 5.7 CONNECTIONS 161 5.7.1
APPLICATIONS TO ALGEBRAIC LOGIC 161 5.7.2 APPLICATIONS TO OTHER LOGICS
165 MULTI-DIMENSIONAL SEMANTICS FOR EVERY MODAL LANGUAGE 169 6.1 LOGICS
WITH ONE MODALITY 169 6.2 LOGICS WITH ARBITRARY MANY MODALITIES 172 6.3
VERSATILE SIMILARITY TYPES 176 6.4 THE MODAL LOGIC OF COMPOSITION AND
ITS CONJUGATES 176 OPEN PROBLEMS 181 APPENDICES - 185 A MODAL SIMILARITY
TYPES 185 A.1 INTRODUCTION 185 A.2 MODAL SIMILARITY TYPES 186 A.3
FRAMES, MODELS AND CORRESPONDENCE 187 A.4 STRUCTURAL FRAME OPERATIONS
188 A.5 BOOLEAN 5-ALGEBRAS 190 A.6 FRAMES AND ALGEBRAS 192 A.7 MODAL
LOGICS AND DERIVATION SYSTEMS 193 A.8 ALGEBRAIC DERIVATIONS 196 A.9
CANONICAL STRUCTURES 196 B A MODAL TOOLKIT 199 B.I SAHLQVIST THEORY 199
B.I.I DEFINITIONS 200 B.I.2 SAHLQVIST CORRESPONDENCE 202 B.I.3
CANONICITY & COMPLETENESS 203 B.I.4 ALGEBRAIC ASPECTS OF SAHLQVIST
THEORY 204 B.2 LOGICAL OPERATORS 205 B.2.1 THE UNIVERSAL MODALITY 205
B.2.2 VERSATILE SIMILARITY TYPES 207 B.2.3 THE D-OPERATOR . . 208 B.3
NEGATIVE DEFINABILITY AND UNORTHODOX AXIOMATICS 210 B.4 INTERPOLATION
214 B.5 FILTRATIONS 217 B.6 A LOCAL AND A GLOBAL PARADIGM 220
BIBLIOGRAPHY 223 LIST OF SYMBOLS 233 INDEX 237
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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 Philosophie |
| format | Book |
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| id | DE-604.BV011375269 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:08:40Z |
| institution | BVB |
| isbn | 079234345X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007644450 |
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| physical | XIII, 239 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Kluwer |
| record_format | marc |
| series | Applied logic series |
| series2 | Applied logic series |
| spelling | Marx, Maarten Verfasser aut Multi dimensional modal logic by Maarten Marx and Yde Venema Multi-dimensional modal logic Dordrecht [u.a.] Kluwer 1997 XIII, 239 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied logic series 4 Modality (Logic) Modallogik (DE-588)4074914-9 gnd rswk-swf Modallogik (DE-588)4074914-9 s DE-604 Venema, Yde Verfasser aut Applied logic series 4 (DE-604)BV011076498 4 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007644450&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Marx, Maarten Venema, Yde Multi dimensional modal logic Applied logic series Modality (Logic) Modallogik (DE-588)4074914-9 gnd |
| subject_GND | (DE-588)4074914-9 |
| title | Multi dimensional modal logic |
| title_alt | Multi-dimensional modal logic |
| title_auth | Multi dimensional modal logic |
| title_exact_search | Multi dimensional modal logic |
| title_full | Multi dimensional modal logic by Maarten Marx and Yde Venema |
| title_fullStr | Multi dimensional modal logic by Maarten Marx and Yde Venema |
| title_full_unstemmed | Multi dimensional modal logic by Maarten Marx and Yde Venema |
| title_short | Multi dimensional modal logic |
| title_sort | multi dimensional modal logic |
| topic | Modality (Logic) Modallogik (DE-588)4074914-9 gnd |
| topic_facet | Modality (Logic) Modallogik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007644450&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT marxmaarten multidimensionalmodallogic AT venemayde multidimensionalmodallogic |