Dual Tableaux: Foundations, Methodology, Case Studies
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Springer
2011
|
| Series: | Trends in logic
33 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 495 - 517 |
| Physical Description: | XVI, 523 S. graph. Darst. |
Staff View
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Record in the Search Index
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IMAGE 1
CONTENTS
PART I FOUNDATIONS
1 DUAL TABLEAU FOR CLASSICAL FIRST-ORDER
LOGIC. 3
1.1 INTRODUCTION 3
1.2 CLASSICAL FIRST-ORDER LOGIC WITH IDENTITY 4
1.3 RASIOWA-SIKORSKI PROOF SYSTEM FOR C1ASSICAL FIRST-ORDER LOGIC WITH
IDENTITY 5
1.4 TABLEAU SYSTEM FOR CLASSICAL FIRST-ORDER LOGIC WITH IDENTITY . . .
. 12 1.5 QUASI PROOF TREES . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.6 DUALITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.7 TRANSFORMATION OF PROOFS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 19
1.8 DISCUSSION OF VARIOUS RULES FOR IDENTITY 19
1.9 DUAL TABLEAUX AND HILBERT-STYLE SYSTEMS 22
1.10 DUAL TABLEAUX AND GENTZEN-STY LE SYSTEMS. . . . . . . . . . . . . .
. . . . . . . . . . . 24
1.11 DUAL TABLEAUX AND DUAL RESOLUTION 27
2 DUAL TABLEAUX FOR LOGICS OF C1ASSICAL AIGEBRAS OF BINARY RELATIONS. .
33 2.1 INTRODUCTION 33
2.2 ALGEBRAS OF BINARY RELATIONS. . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 34
2.3 LOGICS OF BINARY RELATIONS. . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 36
2.4 RELATIONAL DUAL TABLEAUX . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 38
2.5 A BASIC RELATIONAL LOGIC . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 39
2.6 A METHOD OF PROVING SOUNDNESS AND COMPLETENESS OFRELATIONAL DUAL
TABLEAUX 43
2.7 RELATIONAL LOGIC WITH RELATIONS I AND I' 45
2.8 DISCUSSION OF VARIOUS RULES FOR RELATION I' . . . . . . . . . . .
. 50
2.9 FULL RELATION ALGEBRAS AND RELATIONAL LOGICS 54
2.10 AN EXAMPLE OF A RELATIONAL DUAL TABLEAU PROOF 55
2.11 RELATIONAL ENTAILMENT. . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 61
2.12 DECISION PROCEDURES FOR SOME RELATIONAL LOGICS . . . . . . . . .
. . . . . . . 62
XI
IMAGE 2
XII CONTENTS
3 THEORIES OF POINT RELATIONS AND RELATIONAL MODEL CHECKING. . . . . .
. . . . 69 3.1 INTRODUCTION 69
3.2 RELATIONAL LOGICS WITH POINT RELATIONS INTRODUCED WITH AXIOMS. 70
3.3 RELATIONAL LOGICS WITH POINT RELATIONS INTRODUCED WITH DEFINITIONS.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 72
3.4 MODEL CHECKING IN RELATIONAL LOGICS 75
3.5 VERIFICATION OF SATISFACTION IN RELATIONAL LOGICS . . . . . . . . 80
PART 11 REASONING IN LOGICS OF NON-CLASSICAL AIGEBRAS OF RELATIONS
4 DUAL TABLEAUX FOR PEIRCE AIGEBRAS 85
4.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 85
4.2 PEIRCE ALGEBRAS 86
4.3 PEIRCE LOGIC . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 87
4.4 DUAL TABLEAU FOR PEIRCE LOGIC 88
4.5 ENTAILMENT, MODEL CHECKING, AND SATISFACTION IN PEIRCE LOGIC 93 4.6
PEIRCE ALGEBRAS AND TERMINOLOGICAL LANGUAGES 99
5 DUAL TABLEAUX FOR FORK AIGEBRAS 105
5.1 INTRODUCTION 105
5.2 FORK AIGEBRAS 106
5.3 FORK LOGIC 108
5.4 DUAL TABLEAU FOR FORK LOGIC 110
5.5 RELATIONAL INTERPRETATION OF FIRST-ORDER THEORIES 116
6 DUAL TABLEAUX FOR RELATIONAL DATABASES 121
6.1 INTRODUCTION 121
6.2 THE CALCULUS OF TYPED RELATIONS 122
6.3 A LOGIC OFTYPED RELATIONS 125
6.4 DUAL TABLEAU FOR THE LOGIC OF TYPED RELATIONS 127
6.5 RELATIONAL REPRESENTATION OF DATABASE DEPENDENCIES 132
6.6 DUAL TABLEAU FOR DATABASE DEPENDENCIES 135
PART 111 RELATIONAL REASONING IN TRADITIONAL NONC1ASSICAL LOGICS
7 DUAL TABLEAUX FOR CLASSICAL MODAL LOGICS 143
7.1 INTRODUCTION 143
7.2 CLASSICAL PROPOSITIONAL LOGIC 144
7.3 PROPOSITIONAL MODAL LOGICS 144
7.4 RELATIONAL FORMALIZATION OF MODAL LOGICS 146
7.5 DUAL TABLEAUX FOR STANDARD MODAL LOGICS 151
7.6 ENTAILMENT IN MODAL LOGICS 153
7.7 MODEL CHECKING IN MODAL LOGICS 156
7.8 VERIFICATION OF SATISFACTION IN MODAL LOGICS 157
IMAGE 3
CONTENTS
XIII
8 DUAL TABLEAUX FOR SO ME LOGICS BASED ON INTUITIONISM 161
8.1 INTRODUCTION 161
8.2 RELATIONAL FORMALIZATION OF INTUITIONISTIC LOGIC 162
8.3 RELATIONAL FORMALIZATION OF MINIMALLNTUITIONISTIC LOGIC 167
8.4 RELATIONAL FORMALIZATION OF SOME INTERMEDIATE LOGICS 171
8.5 RELATIONAL FORMALIZATION OF A LOGIC FOR HARDWARE VERIFICATION 174
9 DUAL TABLEAUX FOR RELEVANT LOGICS 177
9.1 INTRODUCTION 177
9.2 RELEVANT LOGICS 178
9.3 TRANSLATION OF RELEVANT LOGICS INTO RELATIONAL LOGICS 179
9.4 RELATIONAL DUAL TABLEAU FOR LOGIC RLV .,.,.,.,.,.,., .
.,.,.,.,.,.,., 183 9.5 RELATIONAL DUAL TABLEAUX FOR AXIOMATIC EXTENSIONS
OF LOGIC RLV . ., . ., ., ., . ., .,., ., ., . ., ., . ., .
., ., . ., ., ., ., ., 189
10 DUAL TABLEAUX FOR MANY. VALUED LOGICS 195
10.1 INTRODUCTION 195
10.2 FINITELY MANY-VALUED LOGICS 196
10.3 RELATIONAL FORMALIZATION OF FINITELY MANY- VALUED LOGICS 199 10.4
DUAL TABLEAUX FOR FINITELY MANY- VALUED LOGICS 204
10.5 THREE- VALUED LOGICS 208
PART IV RELATIONAL REASONING IN LOGICS OF INFORMATION AND DATA ANALYSIS
11 DUAL TABLEAUX FOR INFORMATION LOGICS OF PLAIN FRAMES 217
11.1 INTRODUCTION .,., ., .,.,.,.,.,.,., .,.,., 217
11.2 INFORMATION SYSTEMS 218
11.3 INFORMATION LOGICS NIL AND IL . .,.,., . ., . .,.,., ., . ., . .,
. .,.,., .,223
11.4 RELATIONAL FORMALIZATION OF LOGICS NIL AND IL 225
11.5 INFORMATION LOGIC CI AND ITS RELATIONAL FORMALIZATION 231
12 DUAL TABLEAUX FOR INFORMATION LOGICS OF RELATIVE FRAMES 237
12.1 INTRODUCTION 237
12.2 RELATIVE FRAMES 238
12.3 RELATIONAL FORMALIZATIONS OF THE LOGICS OF STRONG AND WEAK RELATIVE
FRAMES 240
12.4 RELATIONAL FORMALIZATION OF THE LOGIC RARE-NIL 245
12.5 RELATIONAL FORMALIZATION OF THE LOGIC RARE-CI 247
12.6 RELATIONAL FORMALIZATION OF THE LOGIC OF STRONG COMPLEMENTARITY
FRAMES 249
13 DUAL TABLEAU FOR FORMAL CONCEPT ANALYSIS 251
13.1 INTRODUCTION 251
13.2 BASIC NOTIONS OFFORMAL CONCEPT ANALYSIS 251
13.3 CONTEXT LOGIC AND ITS DUAL TABLEAU .,., . .,., . ., . ., .
.,.,., . .,.,.,.253
13.4 ENTAILMENT, MODEL CHECKING, AND SATISFACTION IN CONTEXT LOGIC .
257
IMAGE 4
XIV CONTENTS
14 DUAL TABLEAU FOR A FUZZY LOGIC 263
14.1 INTRODUCTION 263
14.2 MTL-ALGEBRAS 264
14.3 THE LOGIC MTL 264
14.4 RELATIONAL FORMALIZATION OFLOGIC MTL 266
IS DUAL TABLEAUX FOR LOGICS OF ORDER OF MAGNITUDE REASONING 277 15.1
INTRODUCTION 277
15.2 A MULTIMODAL LOGIC OFORDER OFMAGNITUDE REASONING 278
15.3 DUAL TABLEAU FOR THE LOGIC OF ORDER OF MAGNITUDE REASONING 280
PART V RELATIONAL REASONING ABOUT TIME, SPACE, AND ACTION
16 DUAL TABLEAUX FOR TEMPORAL LOGICS 291
16.1 INTRODUCTION 291
16.2 BASIC TEMPORAL LOGIC 292
16.3 SEMANTIC RESTRICTIONS ON BASIC TEMPORAL LOGIC 294
16.4 TEMPORAL LOGICS WITH SINCE AND UNTIL 300
16.5 STANDARD TEMPORAL LOGICS WITH NOMINALS 306
16.6 TEMPORAL INFORMATION LOGICS 311
17 DUAL TABLEAUX FOR INTERVAL TEMPORAL LOGICS 315
17.1 INTRODUCTION 315
17.2 HALPERN-SHOHAM LOGIC 316
17.3 RELATIONAL LOGIC FOR HALPERN-SHOHAM LOGIC 317
17.4 TRANSLATION OF HALPERN-SHOHAM LOGIC INTO A RELATIONAL LOGIC 318
17.5 DUAL TABLEAU FOR HALPERN-SHOHAM LOGIC 320
17.6 DUAL TABLEAUX FOR OTHER INTERVAL TEMPORAL LOGICS 325
18 DUAL TABLEAUX FOR SPATIAL REASONING 329
18.1 INTRODUCTION 329
18.2 DUAL TABLEAUX FOR SPATIAL THEORIES BASED ON A PLAIN CONTACT
RELATION 330
18.3 DUAL TABLEAUX FOR SPATIAL THEORIES BASED ON A CONTACT RELATION ON A
BOOLEAN ALGEBRA 339
18.4 DUAL TABLEAU FOR REGION CONNECTION CALCULUS 348
18.5 DUAL TABLEAUX FOR SPATIAL THEORIES OF PROXIMITY RELATION 354
19 DUAL TABLEAUX FOR LOGICS OFPROGRAMS 359
19.1 INTRODUCTION 359
19.2 RELATIONAL FORMALIZATION OF PROPOSITIONAL DYNAMIC LOGIC 360 19.3
RELATIONAL FORMALIZATION OF DYNAMIC LOGIC WITH PROGRAM SPECIFICATIONS
366
19.4 RELATIONAL FORMALIZATION OF LOGICS OF DEMONIC NONDETERMINISTIC
PROGRAMS 371
19.5 RELATIONAL FORMALIZATION OF EVENT STRUCTURE LOGICS 376
IMAGE 5
CONTENTS
PART VI BEYOND RELATIONAL THEORIES
XV
20 DUAL TABLEAUX FOR THRESHOLD LOGICS 385
20.1 INTRODUCTION 385
20.2 THRESHOLD LOGICS 385
20.3 DUAL TABLEAUX FOR THRESHOLD LOGICS 388
20.4 MUTUALINTERPRETABILITY OF A THRESHOLD LOGIC AND CLASSICAL
FIRST-ORDER LOGIC 393
21 SIGNED DUAL TABLEAU FOR GDEL-DUMMETT LOGIC 397
21.1 INTRODUCTION 397
21.2 GDEL-DUMMETT LOGIC 398
21.3 SIGNED DUAL TABLEAU DECISION PROCEDURE FOR GDEL-DUMMETT LOGIC 398
22 DUAL TABLEAUX FOR FIRST-ORDER POST LOGICS .407
22.1 INTRODUCTION 407
22.2 POST AIGEBRAS OF ORDER N .407
22.3 FIRST-ORDER N-VALUED POST LOGIC .408
22.4 DUAL TABLEAUX FOR POST LOGICS .,.,.,.,.,.,.,.,., . .,.,.,., .,.,.,
.,410
23 DUAL TABLEAU FOR PROPOSITIONAL LOGIC WITH IDENTITY 417
23.1 INTRODUCTION 417
23.2 A PROPOSITIONAL LOGIC WITH IDENTITY .418
23.3 AXIOMATIC EXTENSIONS OF THE PROPOSITIONAL LOGIC WITH IDENTITY .420
23.4 DUAL TABLEAU FOR THE PROPOSITIONAL LOGIC WITH IDENTITY .424
23.5 DUAL TABLEAUX FOR AXIOMATIC EXTENSIONS OF THE PROPOSITIONAL LOGIC
WITH IDENTITY .428
24 DUAL TABLEAUX FOR LOGICS OF CONDITIONAL DECISIONS .433
24.1 INTRODUCTION 433
24.2 LOGIC OF CONDITIONAL DECISIONS AND ITS DUAL TABLEAU DECISION
PROCEDURE .434
24.3 AIGEBRAS OF CONDITIONAL DECISIONS .438
24.4 RELATIONAL INTERPRETATION OF THE LOGIC OF CONDITIONAL DECISIONS .
.441 24.5 LOGICS OF CONDITIONAL DECISIONS OF ORDER N AND THEIR DUAL
TABLEAU DECISION PROCEDURES .444
PART VII CONCLUSION
25 METHODOLOGICAL PRINCIPLES OF DUAL TABLEAUX 455
25.1 INTRODUCTION 455
25.2 THEORIES INTERPRETED RELATIONALLY .456
25.3 RELATIONAL LOGICS .458
25.4 RELATIONAL LANGUAGES VERSUS FIRST-ORDER LANGUAGES .460
IMAGE 6
XVI
25.5
25.6 25.7 25.8 25.9
25.10 25.11 25.12
CONTENTS
DUAL TABLEAUX 461
CONSTRAINT-RULE CORRESPONDENCE .463
DEFINITION-RULE CORRESPONDENCE .468
BRANCH MODEL AND COMPLETENESS PROOF .473
ALTERNATIVE FORMS 01' RULES .476
IMPLEMENTATIONS .487
TOWARDS DECISION PROCEDURES .492
CONCLUSION .492
REFERENCES .495
INDEX 519 |
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| indexdate | 2024-07-20T11:07:26Z |
| institution | BVB |
| language | English |
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| physical | XVI, 523 S. graph. Darst. |
| publishDate | 2011 |
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| publisher | Springer |
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| series | Trends in logic |
| series2 | Trends in logic |
| spelling | Orłowska, Ewa 1935- Verfasser (DE-588)122556100 aut Dual Tableaux Foundations, Methodology, Case Studies Ewa Orlowska ; Joanna Golińska-Pilarek Dordrecht [u.a.] Springer 2011 XVI, 523 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Trends in logic 33 Literaturverz. S. 495 - 517 Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Logikkalkül (DE-588)4353514-8 gnd rswk-swf Deduktion (DE-588)4011271-8 gnd rswk-swf Deduktion (DE-588)4011271-8 s Logikkalkül (DE-588)4353514-8 s DE-604 Mathematische Logik (DE-588)4037951-6 s Golińska-Pilarek, Joanna 1976- Verfasser (DE-588)1176732110 aut Trends in logic 33 (DE-604)BV011512969 33 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3524305&prov=M&dok_var=1&dok_ext=htm Inhaltstext V:DE-604 application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022539815&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Orłowska, Ewa 1935- Golińska-Pilarek, Joanna 1976- Dual Tableaux Foundations, Methodology, Case Studies Trends in logic Mathematische Logik (DE-588)4037951-6 gnd Logikkalkül (DE-588)4353514-8 gnd Deduktion (DE-588)4011271-8 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4353514-8 (DE-588)4011271-8 |
| title | Dual Tableaux Foundations, Methodology, Case Studies |
| title_auth | Dual Tableaux Foundations, Methodology, Case Studies |
| title_exact_search | Dual Tableaux Foundations, Methodology, Case Studies |
| title_full | Dual Tableaux Foundations, Methodology, Case Studies Ewa Orlowska ; Joanna Golińska-Pilarek |
| title_fullStr | Dual Tableaux Foundations, Methodology, Case Studies Ewa Orlowska ; Joanna Golińska-Pilarek |
| title_full_unstemmed | Dual Tableaux Foundations, Methodology, Case Studies Ewa Orlowska ; Joanna Golińska-Pilarek |
| title_short | Dual Tableaux |
| title_sort | dual tableaux foundations methodology case studies |
| title_sub | Foundations, Methodology, Case Studies |
| topic | Mathematische Logik (DE-588)4037951-6 gnd Logikkalkül (DE-588)4353514-8 gnd Deduktion (DE-588)4011271-8 gnd |
| topic_facet | Mathematische Logik Logikkalkül Deduktion |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3524305&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022539815&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011512969 |
| work_keys_str_mv | AT orłowskaewa dualtableauxfoundationsmethodologycasestudies AT golinskapilarekjoanna dualtableauxfoundationsmethodologycasestudies |