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This webpage contains a free downloadable version of my lecture notes on Logic and Games, written for a course that was taught at the ILLC Amsterdam and other locations from 1999 to 2003. The title of these notes suggests two directions that occur intertwined in the text: 'Logic as Games' through games that analyze logical truth or consequence, and 'Logic of Games' in the form of logical analysis of arbitrary games. The two perspectives have many points of contact -- or at least, that conviction underlies this course.
In the time since these lecture notes were used, no standard textbook has appeared covering all these topics, so it seemed a good idea to make this material available. The text has been very lightly edited for typography and references, but it is essentially the original version. Even so, researchwise, much has happened since 2003, continuing discussions or issues raised in these lectures. The second offering on this website is a more or less complete series of papers that I have written on these topics up until 2011.
I am currently working on a monograph "Logic in Games", to appear with Springer Science Publishers, Lecture Notes in AI. It will use only a selection from this course material and the follow-up papers -- and therefore, this free publication serves as a supplement.
There is much more going on at the interface of logic and game theory, beyond the topics posted here. Here are some websites documenting recent publications and relevant events (LORIweb), key conferences (TARK, LOFT) as well as book series (Texts in Logic and Games).
Johan van Benthem, Amsterdam, September 2011
Papers
| 1988 1990 1999 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 |
| 1988 |
|---|
Games in Logic. In J. Hoepelman, ed., Representation
and Reasoning. Niemeyer Verlag,
Tübingen, pags 3-15. [An early survey
including some less-known games.] |
| 1990 |
|
Computation versus Play as a Paradigm for Cognition.
Acta Philosophica Fennica 49, pags 236-251.
[Would games be a better paradigm for cognition
than machines?] |
| 1999 |
|
Interpolation, Preservation,
and Pebble Games. Journal
of Symbolic Logic 64:2, pags 881-903. [with Jon Barwise].
(Text available). [Infinite
games and fixed-point definability.] |
| 2001 |
|
Action and Procedure in Reasoning. Cardozo Law Review 22, pags 1575-1593.
(Text available). [Possible uses of game models for capturing the essence
of legal procedure.] |
|
Games in Dynamic Epistemic
Logic. Bulletin of Economic
Research (Proceedings LOFT-4, Torino) 53:4,
pags 219-248. [Analyzing games of imperfect information as models for
modal-epistemic logic, at both a finer level of action and a coarser level
of strategy-based powers.] |
| 2002 |
|
Extensive Games as
Process Models. Journal of
Logic, Language and Information 11:3,
pags 289-313. [Games as multi-agent processes studied by standard techniques
from computational logic.] |
| 2003 |
|
A Modal Walk through Space. Journal of Applied Non-Classical Logic 12:3-4,
pags 319-363. [with Marco Aiello]. (Text available). [New
modal bisimulation games on topological spaces.] |
|
Logic and Game Theory: close encounters of the
third kind. In G. Mints and R. Muskens,
eds., Games, Logic, and Constructive Sets.
CSLI Publications, Stanford, pags 3-22. [How logic and game theory can meet at different levels
of analysis.] |
|
Logic Games are Complete
for Game Logics. Studia Logica
75, pags 183-203. (Text available).
[Evaluation games for modal or first-order
logic, a natural but very special class, capture the complete algebra of
arbitrary sequential game operations.] |
| 2004 |
|
De Kunst van het Vergaderen. In Wiebe van der Hoek, ed., Liber Amicorum 'John-Jules Charles Meijer 50'.
Onderzoeksschool SIKS, Utrecht, pags 5-7. [How modeling real argumentation involves games with
dynamics of arguments losing value over time.] |
|
Diversity of Logical Agents in Games. Philosophia Scientiae 8:2,
pags 163-178. [with Fenrong Liu]. (Text available). [Game
analysis need not make uniform assumptions about players. Specific update
rules such as those of dynamic-epistemic logic correspond, via a representation
theorem, to properties of perfect recall and no miracles.] |
|
Probabilistic Features
in Logic Games (invited presentation, Open
Court Symposium, APA Chicago). In D. Kolak
and J. Symons, eds., Quantifiers, Questions,
and Quantum Physics. Springer Verlag,
New York, pags 189-194.
[How IF games invite standard game-theoretic
solution procedures, replacing truth values by numerical equilibria in mixed
strategies.] |
| 2005 |
|
An Essay on Sabotage and Obstruction. In
D. Hutter, eds., Mechanizing Mathematical Reasoning, Essays in Honor
of Jörg Siekmann on the Occasion of his 69th Birthday. Springer Verlag, ,
pags 268 - 276. (Text
available). [Transforming
standard algorithms under adverse circumstances into games with systematic
opposition, analyzed as new modal logic of model change.] |
|
L'Art et la Logique de la Conversation.
Dossier Logique. Èditions Pour la Science, Paris, pags 68-73.
[Introduction to logic and intelligent interaction
for a general audience.] |
|
Open Problems in Logic and Games. In
S. Artemov, H. Barringer, A. d'Avila Garcez, L.
Lamb and J. Woods, eds., Essays in
Honour of Dov Gabbay. King's College
Publications, London, pags 229-264. (Text available). [A
list of challenges, many of them still unsolved.] |
| 2006 |
|
Logical Construction Games. In T. Aho and A.-V. Pietarinen, eds., Truth and Games, essays in honour of Gabriel Sandu.
Acta Philosophica Fennica 78, , pags 123-138. (Text available). [Turning
semantic tableaus into two-player games of model construction makes proofs
and models live in harmony.] |
|
Preference Logic, Conditionals, and Solution Concepts
in Games. In H. Lagerlund, S. Lindström
and R. Sliwinski, eds., Modality Matters.
University of Uppsala, Uppsala, pags 61-76. [with
Sieuwert van Otterloo and Olivier Roy].
(Text available). [Defining
the Backward Induction strategy as the unique relation in extensive games
that satisfies a natural modally definable rationality property.] |
|
The Epistemic Logic of IF Games. In
R. Auxier and L. Hahn, eds., The Philosophy of Jaakko Hintikka (Schilpp Series).
Open Court Publishers, Chicago, pags 481-513.
(Text available). [Analyzing
IF games as special games of imperfect information supporting a standard
modal-epistemic language, and investigating what would make them playable.]
|
| 2007 |
|
Rationalizations and Promises in Games.
Philosophical Trends ('supplement 2006' on logic), pags 1-6. (Text available). [Various
scenarios for changing games using dynamic-epistemic logics.] |
|
Interview. In V. Hendricks and P. Hansen, eds., Game Theory: 5 Questions. Automatic Press, Copenhagen,
pags 9-19. (Text
available). [A
general programmatic view.] |
|
Logic Games, From Tools to Models of Interaction.
In A. Gupta, R. Parikh and J. van Benthem,
eds., Logic at the Crossroads. Allied Publishers, Mumbai,
pags 283-317. (Text
available). [A
survey of existing logic games emphasizing general features connecting them,
while raising new issues at the interface with further game-theoretic structure.]
|
|
Rational Dynamics
and Epistemic Logic in Games. International Game Theory Review 9:1,
pags 13-45. (Erratum
reprint, 9:2,
pags 377-409). (Text available). [Game
solution proocedures analyzed as a locus of rationality in its own right,
using dynamic-epistemic logics of iterated public announcements, with limit
models that are definable in modal fixed-point logics.] |
| 2008 |
|
Computation as Conversation.
In S. Cooper, B. Löwe & A. Sorbi, eds.,
New Computational Paradigms, Changing
Conceptions of What is Computable. Springer, New York,
pags 35-58. (Text
available). [Conversation
may be viewed as computation in dynamic epistemic logics, but conversely,
computation may also be viewed as conversation. These dual perspectives
are held together from a logical point of view by notions such
as multi-agent strategies and the importance of 'gamifying' existing algorithms.]
|
|
Games that Make Sense: logic, language and multi-agent
interaction. In K. Apt and R. van Rooij,
eds., New Perspectives on Games and Interaction
(volume 4 of Texts in Logic and Games). Amsterdam University Press, Amsterdam, pags 197-209.
(Text available). [A
survey of the different kinds of games that exist by now for analyzing the
emergence of meaning, performing evaluation, or engaging in discourse.]
|
|
Modeling Simultaneous
Games in Dynamic Logic. Synthese
(KRA) 165:2, pags 247-268. [with Sujata
Ghosh and Fenrong Liu]. (Text available). [Extending
Parikh's dynamic game logic of sequential game constructions to simple operators
for concurrency.] |
| 2009 |
|
Decisions, Actions, and Games, a logical
perspective. In R. Ramanujam and Sundar
Sarukkai, eds., Proceedings of the
Third Indian Conference on Logic and Applications ICLA 2009. Springer (LNAI 5378),
pags 1-22. (Text
available). [Analyzing
Backward Induction as a paradigm for social reasoning, in various logical
scenarios including iterated DEL-style belief revision as plausibility change.]
|
| 2010 |
|
A Logician Looks at Argumentation Theory.
Cogency. 1:2,
Universidad Diego Portales. [How Toulmin's famous "The Uses of Argument" may be seen
as a plea for logical dynamics modeling argumentatie procedure, rather than
a call for abandoning logic altogether.] |
|
Game Solution, Epistemic Dynamics,
and Fixed-Point Logics. Fundamenta
Informaticae. 100, pags
19-41. [with Amélie Gheerbrant]. (Text available). [Being
precise about defining game solutions in the fixed-point logics used in theories
of computation. As a spin-off, the relation is clarified between strategies
and beliefs.] |
|
In Praise of Strategies. In J. van Eijck and R. Verbrugge, eds., Foundations of Social Software, Studies in Logic.
College Publications, pags 283–317. (Text available). [A
survey showing the many places where implicit logics of strategies need the
addition of explicit vocabulary defining strategies to obtain a more realistic
analysis of social reasoning.] |
| 2011 |
|
Exploring a Theory
of Play. In K. R. Apt, ed., Proceedings TARK 2011. pags 12-16. (Text available.) [Games
are often too poor as an input for predicting behavior of their players.
Logic and game theory might meet in a new enterprise containing elements
from both: a 'theory of play'.] |
|
Toward a Theory of Play: A Logical
Perspective on Games and Interaction. GAMES. 2:1, pags
52-86. [with Eric Pacuit & Olivier Roy]. (Text available). [Theory
of play taken further and related to other concerns.] |
|
Logic in a Social Setting. Episteme (P. Weirich, ed., special issue on social
epistemology). To appear. (Text available). |
|
Reasoning and Social Models. Studia Logica (Th. Agotnes, ed., special issue on
on logic and games). To appear. [Issues of 'small modeling' in making sense of games
and social behavior via epistemic-doxastic temporal models.] |