Natural Deduction, Hybrid Systems and Modal Logics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Springer Netherland
2010
|
| Schriftenreihe: | Trends in Logic
30 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXIII, 491 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9789048187843 9789048187850 |
Internformat
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| 245 | 1 | 0 | |a Natural Deduction, Hybrid Systems and Modal Logics |c Andrzej Indrzejczak |
| 264 | 1 | |a Dordrecht [u.a.] |b Springer Netherland |c 2010 | |
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Datensatz im Suchindex
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| adam_text | CONTENTS INTRODUCTION 1 PRELIMINARIES 1.1 CLASSICAL AND FREE LOGIC .
1.1.1 BASIC PROPOSITIONAL LANGUAGE . 1.1.2 THE LANGUAGE OF FIRST-ORDER
LOGIC . 1.1.3 SOME REASONS FOR INTRODUCING FQL . 1.1.4 FORMALIZATION OF
CQLI AND FQLI . 1.1.5 IMPORTANT DERIVED NOTIONS 1.2 DEDUCTIVE SYSTEMS,
RULES, PROOFS . 1.2.1 DEDUCTIVE SYSTEMS 1.2.2 CALCULUS........... 1.2.3
REALIZATION . 1.2.4 EXTENSIONS AND SIMULATIONS 1.2.5 SEMANTICAL SIDE .
1.2.6 TYPES OF DEDUCTIVE SYSTEMS. 2 STANDARD NATURAL DEDUCTION 2.1
ORIGINS OF ND . . . . . . . . 2.2 PRELIMINARY CHARACTERIZATION 2.3 DATA
STRUCTURES .. 2.3.1 F-SYSTEMS .. 2.3.2 S-SYSTEMS.. 2.4 TREES 01
SEQUENCES? 2.4.1 PROBLEMS WITH TREES 2.4.2 PROBLEMS WITH LINEAR PROOFS
2.4.3 SUPPES FORMAT. 2.5 SYSTEM KM . 2.5.1 RULES . XI 1 1 1 4 6 8 14 17
17 18 19 22 24 25 28 29 31 33 33 35 38 38 40 43 45 45 V VI 2.5.2
REALIZATION . . . . . . . . . . . . 2.5.3 DERIVATIONS . . . . . . . . .
. . . 2.5.4 THE ORIGINAL FORMULATION OF KM 2.6 ADEQUACY OF KM ..... 2.7
ND FOR FIRST-ORDER LOGIC . 2.7.1 GENTZEN SYSTEMS . 2.7.2 KALISH/MONTAGUE
RULES FOR CQL 2.7.3 GENTZEN S VARIANT OF KM . 2.7.4 KM FOR FREE LOGIC
..... 2.7.5 INTRODUCTION OF PARAMETERS 2.7.6 GENTZEN S VARIANT OF KMP
2.7.7 KM WITH PARAMETERS FOR FREE LOGIC 2.7.8 IDENTITY . 3 OTHER
DEDUCTIVE SYSTEMS 3.1 SEQUENT SYSTEMS AND TABLEAUX 3.1.1 SEQUENT
CALCULUS . 3.1.2 TABLEAU SYSTEMS . 3.2 RESOLUTION AND DAVIS/PUTNAM
PROCEDURE 3.2.1 RESOLUTION . 3.2.2 DAVIS/PUTNAM SYSTEM . 3.3 CUT AND
COMPLEXITY OF PROOF 4 EXTENDED NATURAL DEDUCTION 4.1 ANALYTIC AND
UNIVERSAL VERSIONS OF ND . 4.1.1 ANALYTICITY . 4.1.2 KE AND ND . 4.2
SYSTEM AND1 .... 4.2.1 HINTIKKA SETS 4.2.2 PROOF SEARCH PROCEDURE FOR
AND1 4.2.3 OPTIMIZATION...... 4.3 SYSTEM AND2 . . . . . . . . . . 4.4
RESOLUTION AND ND COMBINED . 4.4.1 CLAUSES INTRODUCED ... 4.4.2 SYSTEM
RND . . . . . . 4.4.3 SIMULATION OF RESOLUTION AND DP IN RND 4.4.4 RND
FOR FIRST-ORDER LOGIC . . . . . . . . CONTENTS 47 50 53 55 57 57 59 62
64 66 68 72 73 75 76 76 82 85 85 88 89 95 96 98 100 103 106 109
114 115 124 125 128 131 135 CONTENTS VII 5 SURVEY OF MODAL
LOGICS 137 5.1 BASIC MODAL AND TENSE LANGUAGE . 137 5.2 MODAL LOGICS IN
GENERAL . 140 5.3 AXIOMATIC APPROACH TO MODAL LOGICS 143 5.3.1
DEDUCIBILITY . 149 5.4 RELATIONAL SEMANTICS . 150 5.4.1 INTERPRETATION .
152 5.4.2 NORMAL LOGICS 153 5.4.3 EXPRESSIVE STRENGTH OF ORDINARY MODAL
LANGUAGE 155 5.4.4 REGULAR LOGICS 159 5.4.5 WEAK LOGICS 160 5.4.6
ENTAILMENT 162 5.5 COMPLETENESS, DECIDABILITY AND COMPLEXITY 163 5.6
FIRST-ORDER MODAL LOGICS 167 5.6.1 INTRODUCTORY REMARKS 167 5.6.2
IDENTITY 170 5.6.3 SEMANTICS 173 5.6.4 SOME LOGICS . 178 6 STANDARD
APPROACH TO BASIC MODAL LOGICS 182 6.1 STANDARD SEQUENT CALCULI AND
TABLEAU SYSTEMS 183 6.1.1 HISTORICAL REMARKS . 183 6.1.2 STANDARD SC FOR
BASIC MODAL LOGICS 184 6.1.3 SC FOR WEAK BASIC LOGICS 187 6.2 SOME
STANDARD ND FOR MODAL BASIC LOGIC 188 6.2.1 MODAL ASSUMPTIONS 188 6.2.2
MODALIZATION OF RULES 192 6.3 MODALIZATION OF REITERATION RULE 195 6.4
RULES FOR POSSIBILITY .203 6.4.1 ORIGINAL FITCH S SYSTEM .203 6.4.2
FITCH S SYSTEM GENERALIZED .205 6.4.3 MODAL ASSUMPTIONS .209 6.5
STANDARD ND FOR WEAK LOGICS . .211 6.6 FIRST-ORDER MODAL LOGICS .217 7
BEYOND BASIC LOGICS AND STANDARD SYSTEMS 221 7.1 BEYOND BASIC NORMAL
LOGICS .222 7.1.1 ALMOST BA IC LOGICS .223 7.1.2 PROVABILITY LOGICS .224
VIII 7.1.3 LOGICS WITH BRANCHING TS RULES 7.1.4 LOGICS OF LINEAR FRAMES
.. 7.1.5 TEMPORAL LOGICS . 7.2 LIMITATIONS OF STANDARD APPROACH 7.3
REDUNDANCY OF STANDARD SYSTEMS. 7.3.1 ADMISSIBILITY OF PROOF
CONSTRUCTION RULES 7.3.2 INTERDEFINABILITY PROBLEM . 7.4 RND FOR MODAL
LOGICS . 7.4.1 RND SYSTEMS FOR M, RAND K 7.4.2 RND FOR OTHER MODAL
LOGICS 7.5 NONSTANDARD DEDUCTIVE SYSTEMS .. 7.5.1 SEMANTIC TABLEAUX OF
KRIPKE 7.5.2 TABLEAUX WITH BOXES .. 7.5.3 SYSTEMS OF HIGHER LEVEL .. 8
LABELIED SYSTEMS IN MODAL LOGICS 8.1 KINDS OF LABELLING . 8.2 WEAK AND
STRONG LABELLING . . . . 8.2.1 SOME WEAKLY LABELLED SYSTEMS 8.2.2 STRONG
LABELLING . . . . . . . . 8.3 MEDIUM LABELLING - FITTING S APPROACH 8.4
LABELLED ND-K . 8.4.1 LND SYSTEM FOR K . 8.5 OTHER LOGICS . 8.5.1 BASIC
NORMAL LOGICS 8.5.2 REGULAR BASIC LOGICS . 8.5.3 TEMPORAL LOGICS . . .
8.5.4 SOME OTHER LOGICS .. 8.6 LND FOR WEAK MODAL LOGICS 8.7 MRND
SYSTEMS WITH LABELS. 8.7.1 LOCAL LABELLING . 8.7.2 GLOBAL LABELLING
CONTENTS .224 .226 .227 .230 .236 .236 . 241 .244 .244 . 251 .254 .255
.256 .257 259 .260 .263 .263 .267 .269 .273 .273 .278 .278 .279 .280 .2
2 .285 .290 .290 .293 9 LOGICS OF LINEAR FRAMES 297 9.1 DEDUCTIVE
SYSTEMS FOR LOGICS OF LINEAR PRAMES 298 9.1.1 SURVEY OF SYSTEMS 298
9.1.2 A COMPARISON OF SYSTEM S PROPERTIES AND STRATEGIES OF
LINEARIZATION . . 305 9.2 LND-SYSTEM FOR S4.3 312 CONTENTS 9.2.1
CHARACTERISTIC RULE AND ITS CORRECTNESS 9.2.2 EFFICIENCY . 9.3 LND FOR
LINEAR TEMPORAL LOGICS 9.3.1 FORMALIZATION OF KT4.3 .. 9.3.2 OTHER
LINEAR LOGICS ... 9.4 ANALYTIC VERSION OF LND FOR LINEAR LOGICS . 9.5
EXTENSIONS AND LIMITATIONS . 10 ANALYTIC LABELIED ND AND PROOF SEARCH
10.1 ANALYTIC LND . 10.1.1 LABELLED HINTIKKA SETS 10.1.2 BASIC
PROCEDURES 10.2 LOGICS K, D, T . 10.2.1 OPTIMIZATION . 10.3 TRANSITIVE
LOGICS AND LOOP-CONTROL . 10.4 SYMMETRIE AND EUCLIDEAN LOGICS . . 10.4.1
NO TRANSITIVITY . 10.4.2 TRANSITIVE SYMMETRIE OR EUCLIDEAN LOGICS 10.5
LINEAR LOGICS . 10.5.1 FINITE CHAINS . 10.5.2 PROOF SEARCH ALGORITHM
10.5.3 WORST CASE ANALYSIS 11 MODAL HYBRID LOGICS 11.1 HYBRID LOGIC IN
NUTSHELL . 11.1.1 MOTIVATION .... 11.1.2 HISTORICAL REMARKS . 11.2 BASIC
HYBRID LOGIC ..... 11.2.1 BASIC HYBRID LANGUAGE 11.2.2 HYBRID MODELS .
11.2.3 LOGIC . 11.3 COMPLETE HILBERT CALCULI FOR KH@ AND KH 11.4 GENERAL
COMPLETENESS RESULTS .. 11.5 HYBRID TENSE LOGIC . 11.5.1 IMPACT OF PAST
OPERATORS 11.5.2 TENSES . 11.6 LANGUAGE EXTENSIONS . 11.6.1 GLOBAL
MODALITIES 11.6.2 DIFFERENCE MODALITY IX 312 315 317 317 319
.320 326 332 .333 .334 .339 .342 .345 .348 351 351 .354 .356 .357
.359 361 363 .364 .364 .366 .367 .367 .369 .370 371 .374 .379 .379
.380 381 .382 383 X 11.6.3 ILODAL BINDERS 11.6.4 AXIOMATIZATION
11.6.5 EXPRESSIVITY .. 11. 7 MISCELLANEA . . . . . . 11.7.1 FIRST-ORDER
MODAL HYBRID LOGIC QMHL 11.7.2 DECIDABILITY AND COMPLEXITY .... 11.7.3
INTERPOLATION AND BETH DEFINABILITY . CONTENTS .384 .386 .387 .392 .392
.394 .395 12 PROOF METHODS FOR MHL 398 12.1 KINDS OF FORMALIZATION OF
MHL . 399 12.2 SEQUELLT CALCULI . . . . . . . . . . . 400 12.2.1
SELIGMAN S SC . 401 12.2.2 SCQUENT SAT-CALCULUS OF SSLACKBURN . 406
12.2.3 NONSTANDARD SCQUENT CALCULI . 409 12.3 TABLEAU SYSTEMS . . . . .
. . . . 412 12.3.1 ~/1IXED CALCULI . . . . . . . . . . 412 12.3.2
BLACKBURN S SAT-CALCULI . . . . 416 12.3.3 HYBRID SIMULATION OF
BALDONI S STROLLGLY LABELIED T . 420 12.4 ATURAL DEDUCTION SYSTEMS . . .
. . . . 421 12.4.1 STANDARD D-SYSTEMS FOR KH@ . 421 12.4.2 BRAUENER S
ND-SYSTEM . 428 12.5 RESOLUTION. . . . . . . . . . . . . . . . . 434
12.5.1 HYLORES . 434 12.5.2 HRND - HYBRID RND-SYSTEM . 437 BIBLIOGRAPHY
445 INDEX 467
|
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| spelling | Indrzejczak, Andrzej Verfasser aut Natural Deduction, Hybrid Systems and Modal Logics Andrzej Indrzejczak Dordrecht [u.a.] Springer Netherland 2010 XXIII, 491 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Trends in Logic 30 Beweistheorie (DE-588)4145177-6 gnd rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf Logik (DE-588)4036202-4 s Beweistheorie (DE-588)4145177-6 s DE-604 Trends in Logic 30 (DE-604)BV011512969 30 Digitalisierung UB Erlangen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020492321&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Indrzejczak, Andrzej Natural Deduction, Hybrid Systems and Modal Logics Trends in Logic Beweistheorie (DE-588)4145177-6 gnd Logik (DE-588)4036202-4 gnd |
| subject_GND | (DE-588)4145177-6 (DE-588)4036202-4 |
| title | Natural Deduction, Hybrid Systems and Modal Logics |
| title_auth | Natural Deduction, Hybrid Systems and Modal Logics |
| title_exact_search | Natural Deduction, Hybrid Systems and Modal Logics |
| title_full | Natural Deduction, Hybrid Systems and Modal Logics Andrzej Indrzejczak |
| title_fullStr | Natural Deduction, Hybrid Systems and Modal Logics Andrzej Indrzejczak |
| title_full_unstemmed | Natural Deduction, Hybrid Systems and Modal Logics Andrzej Indrzejczak |
| title_short | Natural Deduction, Hybrid Systems and Modal Logics |
| title_sort | natural deduction hybrid systems and modal logics |
| topic | Beweistheorie (DE-588)4145177-6 gnd Logik (DE-588)4036202-4 gnd |
| topic_facet | Beweistheorie Logik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020492321&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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