Abstract
This piece is not a paper reporting on original research, but rather a slightly expanded write-up of some notes for a concluding discussion at the 2012 Workshop on ‘Modeling Strategic Reasoning’ at the Lorentz Center in Leiden, an interdisciplinary meeting on the importance of strategies in many fields, from game theory to linguistics, computer science, and cognitive science, that was the incubator for the present volume on the logic-based analysis of strategies and how we reason with, and about them. My modest purpose here is to highlight a few general, somewhat unresolved, decision points about this proposed program that seemed to resonate with the audience at the Workshop, but that may also present food for thought to a more general reader of this book. The emphasis in the presentation that follows is on logic, a view of strategies that figures prominently in my own work on logic and games, cf. [9]. Still, there are certainly other equally viable and illuminating formal viewpoints on the study of strategies, coming, for instance, from automata theory or dynamical systems, cf. [16, 31].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
I will leave the further ‘modeling’ layer in the title out of consideration altogether.
- 2.
For this level distinction in dynamic-epistemic logics of agency, and what is ‘easy’ and ‘hard’ for acting agents versus for theorists, see also the discussion in [6].
- 3.
Sometimes this is seen as high rationality, but sometimes also as self-serving and not really nice, mirroring the pejorative meaning of ‘strategizing’ in common parlance.
- 4.
In fact, this is exactly what happens when certain sub-communities of game theory, computer science, or AI do attach fixed meanings to some of these terms. Cf. [52].
- 5.
I freely use even further terms, such as ‘plans’ as being more open-ended than strategies, and also, as something one is aware of and commits to, more than strategies.
- 6.
Compare the not wholly unrelated case of epistemology and informational action, where natural language has a rich and telling repertoire of common expressions such as ‘know’, ‘suspect’, ‘learn’, ‘note’, ‘discover’, ‘tell’ that we use with a certain amount of stability and even sophistication when engaging in actions of our own, or reporting and reflecting on actions by others. For more on this theme, cf. [10].
- 7.
As noted before, intuitively, a plan restricts my choices in helpful ways, but it need not fix my behavior uniquely: cf. [20] on the conceptual importance of this ‘slack’.
- 8.
Coalgebraic strategies [54] are typically top-down objects that can be used by making an observation of their head after which an infinite tail of the strategy remains available. This never-ending feature is very different from the bottom-up behavior of terminating programs highlighted in PDL.
- 9.
[11] explores a follow-up to this concrete style of proof analysis for strategic reasoning in infinite games with simultaneous moves.
- 10.
Much further background, including game constructions associated with a strategy calculus in our sense, is found in [9]. That book also discusses how strategies can change our view of logic itself when we move from logic of games to logic as games, reading formulas as complex game expressions.
- 11.
One might seek the robustness already in the standard game-theoretic notion of a strategy, that has to work under every eventuality. One can turn all relevant forms of change into moves in a ‘supergame’, asking for one strategy there. But the latter ‘pre-encoding’ seems far removed from our ordinary understanding of agency.
- 12.
Compare the nice example of repairing programs discussed in [38]. We know very little by way of relevant systematic results in logic. Thus, I am not even aware of model-theoretic preservation theorem under submodels or model extensions for such a simple logic as PDL with programs. However, re-planning in multi-agent systems has been investigated in computer science, cf. [25, 26].
- 13.
Such natural extensions with explicit epistemic features do not seem to exist yet for other logical formats for strategies, such as linear game semantics.
- 14.
This issue plays in the area of epistemic planning (cf. [3]), where different kinds of knowledge or beliefs become important: about where we are in following some current plan, but also beliefs about how we expect the process to develop over time.
- 15.
Similar issues arise in analyzing what it means to understand a formal proof, and useful intuitions might be drawn from our experience with mathematical practice.
- 16.
- 17.
In cognitive reality, zooming out and hiding procedural detail mirror processes of automation turning explicit skills into unconscious routines in the brain, cf. [21].
- 18.
For relevant issues, notions, and results, see the entry on combining logics in the Stanford Encyclopedia of Philosophy [22].
References
Abramsky, S.: Concurrent interaction games. In: Davies, J., Roscoe, A.W., Woodcock, J. (eds.) Millennial Perspectives in Computer Science, pp. 1–12. Palgrave, UK (2000)
Abramsky, S., Jagadeesan, R.: Games and full completeness for multiplicative linear logic. J. Symbolic Logic 59, 543–574 (1992)
Andersen, M.B., Bolander, T., Jensen, M.H.: Conditional epistemic planning. In: del Cerro, L.F., Herzig, A., Mengin, J. (eds.) JELIA 2012. LNCS, vol. 7519, pp. 94–106. Springer, Heidelberg (2012)
Aumann, R.: Backward induction and common knowledge of rationality. Games Econ. Behav. 8, 6–19 (1995)
Axelrod, R.: The Evolution of Cooperation. Basic Books, New York (1984)
van Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press, Cambridge (2011)
van Benthem, J.: In praise of strategies. In: van Eijck, J., Verbrugge, R. (eds.) Games, Actions and Social Software 2010. LNCS, vol. 7010, pp. 96–116. Springer, Heidelberg (2012)
van Benthem, J.: Reasoning about strategies. In: Coecke, B., Ong, L., Panangaden, P. (eds.) Abramsky Festschrift. LNCS, vol. 7860, pp. 336–347. Springer, Heidelberg (2013)
van Benthem, J.: Logic in Games. The MIT Press, Cambridge (2014)
van Benthem, J.: Natural language and logic of agency. J. Logic Lang. Inform. 23(3), 367–382 (2014)
van Benthem, J., Cui, J., Steinert-Threlkeld, S.: Logics for evolutionary games. Working paper, ILLC Amsterdam, Philosophy Stanford, and ILLC Guangzhou (2013)
van Benthem, J., Gerbrandy, J., Hoshi, T., Pacuit, E.: Merging frameworks for interaction. J. Philos. Logic 38, 491–526 (2009)
van Benthem, J., Gheerbrant, A.: Game solution, epistemic dynamics and fixed-point logics. Fundamenta Informaticae 100(1–4), 19–41 (2010)
van Benthem, J., Pacuit, E.: The tree of knowledge in action: towards a common perspective. In: Governatori, G., Hodkinson, I., Venema, Y. (eds.) Proceedings of Advances in Modal Logic (AiML IV), pp. 87–106. King’s College Press, London (2006)
van Benthem, J., Pacuit, E.: Choices, actions, and games. In: MĂ¼ller, T. (ed.) Nuel Belnap on Indeterminism and Free Action. Springer, Dordrecht (2013)
Bicchieri, C., Jeffrey, R., Skyrms, B. (eds.): The Logic of Strategy. Oxford University Press, Oxford (1999)
Binmore, K.: Game Theory: A Very Short Introduction. Oxford University Press, Oxford (2008)
Bonanno, G.: Branching time, perfect information games, and backward induction. Games Econ. Behav. 36, 57–73 (2001)
Brandenburger, A.: Tutorial on game theory. First Amsterdam-Lausanne-London Graduate Workshop, London School of Economics (2007)
Bratman, M.: Shared cooperative activity. Philos. Rev. 101(2), 327–341 (1992)
Calvo, P., Gomila, A. (eds.): Handbook of Cognitive Science. Elsevier, Amsterdam (2009)
Carnielli, W., Coniglio, M.E.: Combining logics. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. Stanford University, spring 2014 edition (2014)
Damasio, A.: The Feeling of What Happens: Body Emotion and the Making of Consciousness. Heinemann, London (1999)
Dunbar, R.I.M., Shultz, S.: Evolution in the social brain. Science 317(5843), 1344–1347 (2007)
Dunin-Kȩplicz, B., Verbrugge, R.: A reconfiguration algorithm for distributed problem solving. Eng. Simul. 18, 227–246 (2001)
Durfee, E.H.: Distributed problem solving and planning. In: Å tÄ›pĂ¡nkovĂ¡, O., Luck, M., MaÅ™Ăk, V., Trappl, R. (eds.) ACAI 2001 and EASSS 2001. LNCS (LNAI), vol. 2086, pp. 118–149. Springer, Heidelberg (2001)
van Eijck, J.: PDL as a multi-agent strategy logic. In: Schipper, B.C. (ed.) TARK 2013: Proceedings of the 14th Conference on Theoretical Aspects of Rationality and Knowledge (2013)
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning About Knowledge. The MIT Press, Cambridge (1995)
Ghosh, S., Ramanujam, R.: Strategies in games: a logic-automata study. In: Bezhanishvili, N., Goranko, V. (eds.) ESSLLI 2010 and ESSLLI 2011. LNCS, vol. 7388, pp. 110–159. Springer, Heidelberg (2012)
Gintis, H.: The Bounds of Reason: Game Theory and the Unification of the Behavioral Sciences. Princeton University Press, Princeton (2008)
Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. Springer, Heidelberg (2002)
Halpern, J., Vardi, M.: The complexity of reasoning about knowledge and time, I: Lower bounds. J. Comput. Syst. Sci. 38, 195–237 (1989)
Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. The MIT Press, Cambridge (2000)
Hintikka, J.: Knowledge and Belief. Cornell University Press, Ithaca (1962)
Hintikka, J., Sandu, G.: Game-theoretical semantics. In: van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language, pp. 361–410. Elsevier, Amsterdam (1997)
Hofbauer, J., Sigmund, K.: Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge (1998)
Holliday, W.: Knowing What Follows; Epistemic Closure and Epistemic Logic. Ph.D. thesis, Department of Philosophy, Stanford University (2012)
Huth, M., Ryan, M.: Logic in Computer Science. Cambridge University Press, Cambridge (2004)
Kooi, B., Tamminga, A.: Conditional obligations in strategic situations. In: Boella, G., Pigozzi, G., Singh, M., Verhagen, H. (eds.) Proceedings 3rd International Workshop on Normative Multi-agent Systems, pp. 188–200 (2008)
Moore, R.: A logic of knowledge and action (1985). Research report
Nozick, R.: Philosophical Explanations. Harvard University Press, Cambridge (1981)
Osborne, M.J., Rubinstein, A.: A Course in Game Theory. The MIT Press, Cambridge (1994)
van Otterloo, S.: A Security Analysis of Multi-Agent Protocols. Ph.D. thesis, ILLC, University of Amsterdam, and Department of Computing, University of Liverpool (2005). DS-2005-05
Pearce, D.G.: Rationalizable strategic behavior and the problem of perfection. Econometrica 52(4), 1029–1050 (1984)
Perea, A.: Epistemic Game Theory: Reasoning and Choice. Cambridge University Press, Cambridge (2012)
Pritchard, D.: Knowledge, Understanding, and Epistemic Value. Cambridge University Press, Cambridge (2009)
Ramanujam, R., Simon, S.: Dynamic logic on games with structured strategies. In: Proceedings 11th International Conference on Principles of Knowledge Representation and Reasoning (KR-08), pp. 49–58. AAAI Press (2008)
Ramanujam, R., Simon, S.: A logical structure for strategies. In: Proceedings Logic and the Foundations of Game and Decision Theory (LOFT7). Texts in Logic and Games, vol. 3, pp. 183–208. Amsterdam University Press (2008)
Roy, O., Anglberger, A., Gratzl, N.: The logic of best actions from a deontic perspective. In: Baltag, A., Smets, S. (eds.) Johan van Benthem on Logic and Information Dynamics. Springer, Dordrecht (2014)
Sandu, G.: An alternative analysis of signaling games. In: Baltag, A., Smets, S. (eds.) Johan van Benthem on Logic and Information Dynamics. Springer, Dordrecht (2014)
Sergot, M.: Norms, action and agency in multi-agent systems. In: Sartor, G., Governatori, G. (eds.) DEON 2010. LNCS, vol. 6181, p. 2. Springer, Heidelberg (2010)
Shoham, Y., Leyton-Brown, K.: Multi-Agent Systems: Algorithmic Game-Theoretic and Logical Foundations. Cambridge University Press, Cambridge (2008)
van der Meyden, R.: The dynamic logic of permission. J. Logic Comput. 6(3), 465–479 (1996)
Venema, Y.: Algebras and co-algebras. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic, pp. 331–426. Elsevier, Amsterdam (2006)
Venema, Y.: Lectures on the modal mu-calculus (2007)
Verbrugge, R.: Logic and social cognition: The facts matter, and so do computational models. J. Philos. Logic 38, 649–680 (2009)
de Weerd, H., Verbrugge, R., Verheij, B.: How much does it help to know what she knows you know? An agent-based simulation study. Artif. Intell. 199, 67–92 (2013)
Acknowledgments
I would like to thank my co-editors Sujata Ghosh and Rineke Verbrugge, as well as the very helpful anonymous reviewers of this volume. I also received valuable feedback from audiences for talks on the theme of designing an explicit logic of strategies.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
van Benthem, J. (2015). Logic of Strategies: What and How?. In: van Benthem, J., Ghosh, S., Verbrugge, R. (eds) Models of Strategic Reasoning. Lecture Notes in Computer Science(), vol 8972. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48540-8_10
Download citation
DOI: https://doi.org/10.1007/978-3-662-48540-8_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-48539-2
Online ISBN: 978-3-662-48540-8
eBook Packages: Computer ScienceComputer Science (R0)