First steps in modal logic:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1994
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIII, 314 S. graph. Darst. |
| ISBN: | 052146482X 9780521464826 9780521057936 |
Staff View
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| 100 | 1 | |a Popkorn, Sally |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a First steps in modal logic |c Sally Popkorn |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1994 | |
| 300 | |a XIII, 314 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804124701252911104 |
|---|---|
| adam_text | Contents
Introduction
xi
Acknowledgements
xiii
I Preliminaries
1
1
Survey of prepositional logic
3
1.1
Introduction
............................. 3
1.2
The language
............................ 4
1.3
Two-valued semantics
........................ 6
1.4
The proof theory
.......................... 7
1.5
Completeness
............................ 9
1.6
Exercises
............................... 11
2
The modal language
13
2.1
Introduction
............................. 13
2.2
The language defined
........................ 15
2.3
Some particular formulas
...................... 16
2.4
Substitution
............................. 17
2.5
Two
remarles
............................ 19
2.6
Exercises
................................ 19
II Transition structures and semantics
23
3
Labelled transition structures
25
3.1
Introduction
...............................25
3.2
Some examples
. .......................· · · 27
3.3
Modal algebras
........................... 28
3.4
Various correspondences
....... . . .-........· ■ ■ . . 30
3.5
The diamond operation
....................... 32
3.6
The structure regained
............. . . ... . ... .34
3.7
Exercises.
......... ... ...... .... ...... . .35
vi
CONTENTS
4
Valuation and satisfaction
39
4.1
Introduction
............................. 39
4.2
The basic satisfaction relation
................... 41
4.3
Some examples
........................... 42
4.4
The three satisfaction relations
.................. 46
4.5
Semantics for modal algebras
................... 48
4.6
Exercises
............................... 51
5
Correspondence theory
61
5.1
Introduction
............................. 61
5.2
Some examples
........................... 61
5.3
The confluence property
...................... 64
5.4
Some non-confluence properties
.................. 66
5.5
Exercises
............................... 69
6
The general confluence result
77
6.1
Introduction
............................. 77
6.2
The structural property
...................... 79
6.3
The set of formulas
......................... 82
6.4
The result
.............................. 83
6.5
Exercises
............................... 84
II! Proof theory and completeness
89
7
Some consequence relations
91
7.1
Introduction
............................ 91
7.2
Semantic consequence
....................... 92
7.3
The problem
............................. 93
7.4
Exercises
...................... _ . . 94
8
Standard formal systems
97
8.1
Introduction
................... 97
8.2
Formal systems defined
. ....... 98
8.3
Some
monomodal
systems
.....................102
8.4
Some
polymodal
systems
............. 106
8.5
Soundness properties
............. 108
8.6
Exercises
..................
HO
9
The general completeness result
119
9.1
Introduction
. . , . ... ........ .119
9.2
Statement of the result
. . . . . . . .... ... .120
9.3
Maximally consistent sets
. . . . .... 121
9.4
The canonical structure
. ... ... . . . . . : [ ■ . 124
9.5
The canonical valuation
.... ....... . . . . .125
CONTENTS
vii
9.6
Proof of the result
.........................126
9.7
Concluding remarks
.........................126
9.8
Exercises
...............................127
10
Kripke-completeness
129
10.1
Introduction
.............................129
10.2
Some canonical systems
......................130
10.3
Confluence induced completeness
.................133
10.4
Exercises
...............................137
IV Model constructions
139
11
Bisimulations
141
11.1
Introduction
.............................141
11.2
Zigzag morphisms
..........................142
11.3
Bisimulations
............................144
11.4
The largest bisimulation
......................147
11.5
A hierarchy of matchings
......................148
11.6
An example
.............................. 150
11.7
Stratified semantic equivalence
...................151
11.8
Exercises
...............................154
12
Filiations
157
12.1
Introduction
.............................157
12.2
The canonical carrying set
.....................159
12.3
The left-most filtration
.......................160
12.4
The right-most filtration
......................161
12.5
Filtrations sandwiched
.......................163
12.6
Separated structures
........................164
12.7
Exercises
...............................166
13
The finite model property
169
13.1
Introduction
.............................169
13.2
The fmp explained
......................... 169
13.3
The classic systems have the fmp
................ . 172
13.4
The basic temporal system has the fmp
.............. 180
13.5
Exercises
.................. .■·.· ........... 182
V More advanced material
185
14
SLL logic
187
14.1
Introduction
..... . . ...... .... .... ........ 187
14.2
The »-closure of a relation
. . . . .
v
. . ........... 189
vüi CONTENTS
14.3
The axioms for SLL
.........................189
14.4
SLL is not canonical
........................191
14.5
A filtration construction
......................193
14.6
The completeness result
......................197
14.7
Exercises
...............................197
15
Lob logic
201
15.1
Introduction
.............................201
15.2
The system defined
.........................206
15.3
The rule of disjunction
.......................206
15.4
The imp
...............................209
15.5
Exercises
...............................214
16
Canonicity without the fmp
217
16.1
Introduction
.............................217
16.2
The system defined
.........................217
16.3
The characteristic properties
....................218
16.4
Canonicity
..............................219
16.5
The finite models
..........................220
16.6
A particular model
.........................222
16.7
Exercises
...............................222
17
Transition structures aren t enough
225
17.1
Introduction
.............................225
17.2
The system KZ
...........................226
17.3
The system KY
...........................227
17.4
A particular structure
.......................228
17.5
Exercises
...............................232
VI Two appendices
235
A The what, why, where.... of modal logic
237
A.I Introduction
. ................ ..........237
A.2 Beginning
................ ..........237
A.3 About this book
...........................239
A.4 What next?
........ . . . .
*
*
.241
A.5 Some uses of modal logic
......................242
В
Some solutions to the exercises
247
B.I Chapter
1. . . .... . . . . . . , _............. 247
B.2 Chapter2
. . . . . ....... ...... .../...... 250
B.3 Chapter
3. . ... ........
M
. . . . .. ....... . . .252
B.4 Chapter
4 ....... . ... ......; !........ . . .254
B.5 Chapters
. . . .:....!. ] !!
І
;
ľCIM* .
. . . . . .260
CONTENTS
ix
B.6
Chapter
6..............................266
B.7
Chapter
7..............................267
B.8 Chapter
8..............................267
B.9 Chapter
9..............................278
B.10 Chapter
10 .............................280
B.ll Chapter
11 .............................286
B.12 Chapter
12 .............................289
B.13 Chapter
13 .............................293
B.14 Chapter
14 .............................299
B.15 Chapter
15 .............................304
B.16 Chapter
16 .............................306
B.17 Chapter
17 .............................308
Bibliography
311
|
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| discipline | Mathematik Philosophie |
| edition | 1. publ. |
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| isbn | 052146482X 9780521464826 9780521057936 |
| language | English |
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| spelling | Popkorn, Sally Verfasser aut First steps in modal logic Sally Popkorn 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1994 XIII, 314 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Modality (Logic) Modallogik (DE-588)4074914-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Modallogik (DE-588)4074914-9 s DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006842668&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Popkorn, Sally First steps in modal logic Modality (Logic) Modallogik (DE-588)4074914-9 gnd |
| subject_GND | (DE-588)4074914-9 (DE-588)4151278-9 |
| title | First steps in modal logic |
| title_auth | First steps in modal logic |
| title_exact_search | First steps in modal logic |
| title_full | First steps in modal logic Sally Popkorn |
| title_fullStr | First steps in modal logic Sally Popkorn |
| title_full_unstemmed | First steps in modal logic Sally Popkorn |
| title_short | First steps in modal logic |
| title_sort | first steps in modal logic |
| topic | Modality (Logic) Modallogik (DE-588)4074914-9 gnd |
| topic_facet | Modality (Logic) Modallogik Einführung |
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