Logic in games:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
MIT Press
2014
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVII, 547 S. graph. Darst. |
| ISBN: | 9780262019903 |
Internformat
MARC
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| 020 | |a 9780262019903 |c hardcover : alk. paper |9 978-0-262-01990-3 | ||
| 035 | |a (OCoLC)876830686 | ||
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| 100 | 1 | |a Benthem, Johan van |d 1949- |e Verfasser |0 (DE-588)124543286 |4 aut | |
| 245 | 1 | 0 | |a Logic in games |c Johan van Benthem |
| 264 | 1 | |a London |b MIT Press |c 2014 | |
| 300 | |a XVII, 547 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Game theory | |
| 650 | 4 | |a Logic | |
| 650 | 0 | 7 | |a Logik |0 (DE-588)4036202-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Spieltheorie |0 (DE-588)4056243-8 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-027181213 | ||
Datensatz im Suchindex
| _version_ | 1804152019597918208 |
|---|---|
| adam_text | Contents
Preface
xv
Introduction
Exploring the Realm of Logic in Games
1
1
Encounters between logic and games
1
2
Logical games
2
3
From logic games to general game structure
5
4
Games as interactive processes
9
5
Logic meets game theory
13
6
From logic and game theory to Theory of Play
23
7
Conclusion
25
8
Contents of this book
26
I Game Logics and Process Structure
31
Introduction to Part I
33
1
Games as Processes: Definability and
Invariance
35
1.1
Games as process graphs in modal logic
36
1.2
Process and game equivalences AS
1.3
Further notions of game equivalence
Ą8
1.4
Conclusion
51
vi
Contents
1.5
Literature
52
2
Preference, Game Solution, and Best Action
53
2.1
Basic preference logic
53
2.2
Relational strategies and options for preference
57
2.3
Defining Backward Induction in fixed point logics
59
2.4
Zooming out to modal logics of best action
61
2.5
Conclusion
63
2.6
Literature
64
2.7
Further directions
6Ą
3
Games with Imperfect Information
67
3.1
Varieties of knowledge in games
67
3.2
Imperfect information games at a glance
69
3.3
Modal-epistemic logic
70
3.4
Correspondence for logical axioms
74
3.5
Complexity of rich game logics
77
3.6
Uncovering the mechanics of the dotted lines
79
3.7
Conclusion
80
3.8
Literature
80
3.9
Further directions
81
4
Making Strategies Explicit
85
4.1
Strategies as first-class citizens
85
4.2
Defining strategies in dynamic logic
86
4.3
General calculus of strategies
91
4.4
Strategies in the presence of knowledge
93
4.5
Conclusion
97
4.6
Literature
98
4.7
Further directions
99
5
Infinite Games and Temporal Evolution
103
5.1
Determinacy generalized
104
5.2
Branching time and temporal logic of powers
106
5.3
Strategizing temporal logic
108
Contents
5.4
Epistemic
and doxastic temporal logics
113
5.5
Conclusion
118
5.6
Literature
119
6
From Games to Models for Games
121
6.1
Some simple scenarios
122
6.2
Different styles of reasoning and modeling choices
123
6.3
Triggers for jumps: Diversity of knowledge in games
125
6.4
Modal logic of game trees
126
6.5
From nodes to histories: Dynamic and temporal logics
128
6.6
Procedural information and
epistemic
forests
129
6.7
Observation uncertainty and imperfect information games
132
6.8
Taking stock: Models of extensive games
132
6.9
Adding beliefs and expectations
136
6.10
From statics of games to dynamics of play
139
6.11
Conclusion
Ц0
6.12
Literature
ЦІ
6.13
Further directions
ЦІ
Conclusion to Part
I 1Ą5
II Logical Dynamics and Theory of Play
Introduction to Part II
1Ą9
7
Logical Dynamics in a Nutshell
151
7.1
Logic as information dynamics
151
7.2
From
epistemic
logic to public announcement logic
153
7.3
From correctness to correction: Belief change and learning
159
7.4
Update by general events with partial observation
165
7.5
Temporal behavior and procedural information
168
7.6
Inference and variety of information
113
7.7
Questions and direction of inquiry
17Ą
viii Contents
7.8
From correct to reasonable: Harmony with evaluation
176
7.9
Conclusion
177
7.10
Literature
178
7.11
Recent developments
178
8
Deliberation as Iterated Update
181
8.1
Backward Induction and announcing rationality
181
8.2
Another scenario: Beliefs and iterated plausibility upgrade
185
8.3
Repercussions and extensions
190
8.4
Logical aspects
193
8.5
Conclusion
197
8.6
Literature
197
9
Dynamic-Epistemic Mechanisms at Play
199
9.1
Retrieving play from a game record
199
9.2
A representation for update on epistemic-temporal models
201
9.3
Tracking beliefs over time
205
9.4
Witnessing events and adding temporal logic
207
9.5
Help is on the way: Hard information during play
210
9.6
Forest murmurs: Soft information during play
213
9.7
Preference change
214
9.8
Dynamics after play
216
9.9
Changing the games themselves
218
9.10
Conclusion
220
9.11
Literature
221
9.12
Further issues
221
10
Toward a Theory of Play
227
10.1
Dynamics in games
227
10.2
Problems of fit: From deliberation to actual play
228
10.3
Forming beliefs from observations
231
10.4
Logical aspects: Models and update actions
235
10.5
Theory of Play
2Ą1
10.6
Locating the necessary diversity
2Ą.2
10.7
Some objections
2ĄĄ
Contents ix
10.8
Living with diversity, linguistic cues, and logical design
245
10.9
Connections and possible repercussions
246
10.10
Conclusion
247
10.11
Literature
241
Conclusion to Part II
2Ą9
III Players Powers and Strategic Games
251
Introduction to Part III
253
11
Forcing Powers
255
11.1
Forcing and strategic powers
255
11.2
Formal conditions and game representation
257
11.3
Modal forcing logic and neighborhood models
258
11.4
Bisimulation,
invariance,
and definability
259
11.5
Digression: Topological models and similarity games
261
11.6
Compositional computation and game algebra
264
11.7
Forcing intermediate positions
264
11.8
Interfacing modal logics of forcing and action
265
11.9
Powers in games with imperfect information
266
11.10
Game transformations and extended logic
269
11.11
Forcing languages, uniform strategies, and knowledge
271
11.12
Conclusion
272
11.13
Literature
273
12
Matrix Games and Their Logics
275
12.1
From trees and powers to strategic matrix forms
275
12.2
Models for strategic games
276
12.3
Matching modal languages
278
12.4
Modal logics for strategic games
280
12.5
General game models, dependence, and correlation
281
12.6
Special logics of best response
282
χ
Contents
12.7
A case study: Rationality assertions, weak and strong
285
12.8
STIT logic and simultaneous action
289
12.9
Conclusion
29Ą
12.10
Literature
294
12.11
Further directions
295
13
Rational Dynamics for Strategic Games
299
13.1
Reaching equilibrium as an
epistemic
process
299
13.2
Iterated announcement of rationality and game solution
302
13.3
From
epistemic
dynamics to fixed point logic
304
13.4
Variations and extensions
307
13.5
Iteration, limits, and abstract fixed point logic for games
308
13.6
Literature
309
Conclusion to Part III
311
IV Logic Games
313
Introduction to Part IV
315
14
Formula Evaluation
317
14.1
Evaluation games for predicate logic
317
14.2
Truth and winning strategies of verifier
319
14.3
Exploring the game view of predicate logic
321
14.4
Game-theoretic aspects of predicate logic
324
14.5
Gamification: Variations and extensions
326
14.6
Conclusion
332
14.7
Literature
333
15
Model Comparison
335
15.1
Isomorphism and first-order equivalence
335
15.2
Ehrenfeucht-Fraïssé
games
337
15.3
Adequacy and strategies
339
15.4
An explicit version: The logic content of strategies
341
Contents xi
15.5
The games in practice: Invariants and special model classes
3Ą3
15.6
Game theory: Determinacy, finite and infinite games
344
15.7
Modifications and extensions
345
15.8
Connections between logic games
347
15.9
Conclusion
З48
15.10
Literature
З49
16
Model Construction
351
16.1
Learning
tableaus
by example
351
16.2
Tableaus,
some general features
355
16.3
Model construction games
356
16.4
The success lemma and some game theory
358
16.5
Making critic more essential: Fragments and variations
359
16.6
Conclusion
362
16.7
Literature
362
17
Argumentation and Dialogue
363
17.1
Dialogue games and actual debate
363
17.2
Learning by playing
365
17.3
Constructive versus classical logic
366
17.4
The logic of the games
369
17.5
Extensions and variations
371
17.6
Conclusion
373
17.7
Literature
373
17.8
Appendix on argumentation
373
18
General Lines through Logic Games
379
18.1
What is gamification?
379
18.2
Calculus of strategies
380
18.3
Game equivalence
381
18.4
Connections between logic games
383
18.5
Operations on logic games
385
18.6
Universal formats: Graph games
386
18.7
Conclusion
388
18.8
Literature
388
xii Contents
18.9
Further directions
388
18.10
Appendix on games in computational logic
390
Conclusion to Part IV
397
V Operations on Games
399
Introduction to Part V
Ą01
19
Dynamic Logic of Sequential Game Operations
Ą.03
19.1
Internal and external views of games
Ą03
19.2
Prom logic games to game logics
ĄOĄ
19.3
Forcing models, games, and game boards
ĄOĄ
19.4
Dynamic game logic All
19.5
Basic game algebra
Ą1Ą
19.6
Bisimulation,
invariance,
and safety
Ą16
19.7
Conclusion
Џ9
19.8
Literature
Ą20
19.9
Further directions
Ą20
20
Linear Logic of Parallel Game Operations
Ą27
20.1
From logic games to game logics, once more
Ą27
20.2
Parallel operations
Ą28
20.3
The games denned
Ą30
20.4
Logical validity of game expressions
Ą32
20.5
Linear logic and resources
Ą32
20.6
An axiom system
Ą35
20.7
Soundness and completeness
Ą36
20.8
Prom proof theory to program semantics
Α3Ί
20.9
Conclusion
Ą38
20.10
Literature
Ą38
20.11
Further directions
Ą39
Conclusion to Part V
ĄĄ3
Contents xiii
VI Comparisons and Merges
ĄĄ.5
Introduction to Part VI
ĄĄ1
21
Logic Games with Imperfect Information
ĄĄ.9
21.1
IF games and imperfect information
449
21.2
The new perspective motivated
451
21.3
The IF language and its games
452
21.4
IF games: Extended examples
454
21.5
IF games, algebra, and logic of imperfect information games
456
21.6
The underlying
epistemic
dynamics
46O
21.7
Conclusion
460
21.8
Literature
461
21.9
Further directions
461
22
Knowledge Games
Ą67
22.1
Group communication on
epistemic
models
467
22.2
Games on
epistemic
models
469
22.3
Announcement games
471
22.4
Question games
472
22.5
Epistemic
games, imperfect information, and protocols
473
22.6
Further logical lines
475
22.7
Conclusion
476
22.8
Literature
476
23
Sabotage Games and Computation
^77
23.1
From algorithms to games: The sabotage game
477
23.2
Logical and computational features
479
23.3
Other interpretations: Learning
4^0
23.4
Computational and game-theoretic aspects of gamification
480
23.5
Logical aspects of sabotage
4$2
23.6
Conclusion
484
23.7
Literature
485
xiv Contents
24 Logic Games
Can Represent Game Logics
Ą87
24.1
Forcing relations and game operations
Ą87
24.2
Forcing bisimulations
Ą88
24.3
Basic game algebra
Ą89
24.4
First-order evaluation games and general game laws
Ą89
24.5
The main result
490
24.6
Discussion
492
24.7
Extensions and desiderata
493
24.8
Literature
494
25
Merging Logic Games with Game Logics
Ą95
25.1
Logical systems with game terms
495
25.2
Tracking a game at different levels
496
25.3
Making games explicit
499
25.4
Making strategies explicit
500
25.5
Logic games as fine structure for game logics
503
25.6
Logic games and game logics entangled
503
25.7
Conclusion
504
Conclusion to Part VI
507
VII
Conclusion
509
Conclusion
511
Bibliography
515
Index
543
|
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| id | DE-604.BV041734495 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:04:03Z |
| institution | BVB |
| isbn | 9780262019903 |
| language | English |
| lccn | 2013015059 |
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| spelling | Benthem, Johan van 1949- Verfasser (DE-588)124543286 aut Logic in games Johan van Benthem London MIT Press 2014 XVII, 547 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Game theory Logic Logik (DE-588)4036202-4 gnd rswk-swf Spieltheorie (DE-588)4056243-8 gnd rswk-swf Logik (DE-588)4036202-4 s Spieltheorie (DE-588)4056243-8 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027181213&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Benthem, Johan van 1949- Logic in games Game theory Logic Logik (DE-588)4036202-4 gnd Spieltheorie (DE-588)4056243-8 gnd |
| subject_GND | (DE-588)4036202-4 (DE-588)4056243-8 |
| title | Logic in games |
| title_auth | Logic in games |
| title_exact_search | Logic in games |
| title_full | Logic in games Johan van Benthem |
| title_fullStr | Logic in games Johan van Benthem |
| title_full_unstemmed | Logic in games Johan van Benthem |
| title_short | Logic in games |
| title_sort | logic in games |
| topic | Game theory Logic Logik (DE-588)4036202-4 gnd Spieltheorie (DE-588)4056243-8 gnd |
| topic_facet | Game theory Logic Logik Spieltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027181213&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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