# Reasoning about coalitional agency and ability in the logics of “bringing-it-about”

- 261 Downloads
- 4 Citations

## Abstract

The logics of “bringing-it-about” have been part of a prominent tradition for the formalization of individual and institutional agency. They are the logics to talk about what states of affairs an acting entity brings about while abstracting away from the means of action. Elgesem’s proposal analyzes the agency of individual agents as the goal-directed manifestation of an individual ability. It has become an authoritative modern reference. The first contribution of this paper is to extend Elgesem’s logic of individual agency and ability to coalitions. We present a general theory and later propose several possible specializations. As a second contribution, we offer algorithms to reason with the logics of bringing-it-about and we analyze their computational complexity.

## Keywords

Logic Bringing-it-about Coalitions Agency Ability Complexity## Notes

### Acknowledgments

I would like to thank Andreas Herzig and Emiliano Lorini, as well as my colleagues at the Laboratory for Applied Ontology for inspiring and commenting earlier presentations of this work. It also greatly benefited from suggestions and corrections of reviewers on previous drafts. This research was funded by a Marie Curie Actions Fellowship FP7 PEOPLE COFUND Trentino.

## References

- 1.Abdou, J., & Keiding, H. (1991). Effectivity functions in social choice. Dordrecht: Kluwer Academic Publishers.Google Scholar
- 2.Alur, R., Henzinger, T. A., & Kupferman, O. (2002). Alternating-time temporal logic.
*The Journal of the ACM*,*49*(5), 672–713.CrossRefMathSciNetGoogle Scholar - 3.Belnap, N., & Perloff, M. (1988). Seeing to it that: A canonical form for agentives.
*Theoria*,*54*(3), 175–199.CrossRefGoogle Scholar - 4.Belnap, N., Perloff, M., & Xu, M. (2001).
*Facing the future (agents and choices in our indeterminist world)*. Oxford: Oxford University Press.Google Scholar - 5.Bottazzi, E., & Ferrario, R. (2011). Critical situations from spontaneous to sophisticated social interactions. In
*New trends in the philosophy of the social sciences, Madrid, 28–29 September 2011*.Google Scholar - 6.Broersen, J., Herzig, A., & Troquard, N. (2006). Embedding alternating-time temporal logic in strategic STIT logic of agency.
*Journal of Logic and Computation*,*16*(5), 559–578.CrossRefMATHMathSciNetGoogle Scholar - 7.Broersen, J., Herzig, A., Troquard, N., & (2007). Normal simulation of coalition logic and an epistemic extension. In
*Proceedings of TARK, 2007*. Brussels, Belgium: ACM DL.Google Scholar - 8.Broersen, J., Herzig, A., & Troquard, N. (2009). What groups do, can do, and know they can do: An analysis in normal modal logics.
*Journal of Applied Non-Classical Logics*,*19*(3), 261–290.CrossRefMATHMathSciNetGoogle Scholar - 9.Brown, M. A. (1988). On the logic of ability.
*Journal of Philosophical Logic*,*17*, 1–26.CrossRefMATHMathSciNetGoogle Scholar - 10.Carmo, J. (2010). Collective agency, direct action and dynamic operators.
*Logic Journal of the IGPL*,*18*(1), 66–98.CrossRefMATHMathSciNetGoogle Scholar - 11.Carmo, J., & Pacheco, O. (2001). Deontic and action logics for organized collective agency modeled through institutionalized agents and roles.
*Fundamenta Informaticae*,*48*, 129–163.MATHMathSciNetGoogle Scholar - 12.Chellas, B. (1969).
*The logical form of imperatives*. Stanford: Perry Lane Press.Google Scholar - 13.Chellas, B. (1980).
*Modal logic: An introduction*. Cambridge: Cambridge University Press.CrossRefMATHGoogle Scholar - 14.Davidson, D. (1967). The logical form of action sentences. In N. Rescher (Ed.),
*The logic of decision and action*. Pittsburgh: University of Pittsburgh Press.Google Scholar - 15.Elgesem, D.:
*Action theory and modal logic*. Ph.D. thesis, Universitetet i Oslo, Oslo (1993).Google Scholar - 16.Elgesem, D. (1997). The modal logic of agency.
*Nordic Journal of Philosophical Logic*,*2*(2), 1–46.MATHMathSciNetGoogle Scholar - 17.Frankfurt, H. (1988).
*The importance of what we care about*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - 18.Goranko, V., Jamroga, W., & Turrini, P. (2013). Strategic games and truly playable effectivity functions.
*Autonomous Agents and Multi-Agent Systems*,*26*, 288–314.CrossRefGoogle Scholar - 19.Governatori, G., & Rotolo, A. (2005). On the axiomatisation of Elgesem’s logic of agency and ability.
*Journal of Philosophical Logic*,*34*, 403–431.CrossRefMATHMathSciNetGoogle Scholar - 20.Halpern, J. Y., & Moses, Y. (1992). A guide to completeness and complexity for modal logics of knowledge and belief.
*Artificial Intelligence*,*54*(2), 319–379.CrossRefMATHMathSciNetGoogle Scholar - 21.Harel, D., Kozen, D., & Tiuryn, J. (2000).
*Dynamic logic*. Cambridge: MIT Press.MATHGoogle Scholar - 22.Herzig, A., & Schwarzentruber, F. (2008). Properties of logics of individual and group agency. In
*Proceeding of advances in modal logic*(pp. 133–149).Google Scholar - 23.Herzig, A., & Troquard, N. (2006). Knowing how to play: Uniform choices in logics of agency. In
*Proceedings of AAMAS, 2006*(pp. 209–216). IFAAMAS.Google Scholar - 24.Horty, J. F. (2001).
*Agency and deontic logic*. Oxford: Oxford University Press.CrossRefMATHGoogle Scholar - 25.Jones, A., & Sergot, M. (1996). A formal characterization of institutionalised power.
*Journal of the IGPL*,*4*(3), 429–445.CrossRefMathSciNetGoogle Scholar - 26.Kanger, S., & Kanger, H. (1966). Rights and parliamentarism.
*Theoria*,*32*, 85–115.CrossRefGoogle Scholar - 27.Kapitan, T. (1996). Incompatibilism and ambiguity in the practical modalities.
*Analysis*,*56*(2), 102–110.CrossRefMATHMathSciNetGoogle Scholar - 28.Kenny, A. (1975).
*Will, freedom and power*. Oxford: Blackwell.Google Scholar - 29.Ladner, R. E. (1977). The computational complexity of provability in systems of modal propositional logic.
*The SIAM Journal on Computing*,*6*(3), 467–480.CrossRefMATHMathSciNetGoogle Scholar - 30.Lindahl, L. (1977).
*Position and change–A study in law and logic*. Dordrecht: D. Reidel.CrossRefGoogle Scholar - 31.
- 32.Miller, S. (2001).
*Social action (a teleological account)*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - 33.Norman, T. J., & Reed, C. (2010). A logic of delegation.
*Artificial Intelligence*,*174*, 51–71.Google Scholar - 34.Pacheco, O., & Carmo, J. (2003). A role based model for the normative specification of organized collective agency and agents interaction.
*Autonomous Agents and Multi-Agent Systems*,*6*, 145–184.CrossRefGoogle Scholar - 35.Pauly, M. (2002). A modal logic for coalitional power in games.
*Journal of Logic and Computation*,*12*(1), 149–166.CrossRefMATHMathSciNetGoogle Scholar - 36.Pörn, I. (1970).
*The logic of power*. Oxford: Blackwell.Google Scholar - 37.Pörn, I. (1977). Action theory and social science: Some formal models. In
*Synthese library*(Vol. 120). Dordrecht: D. Reidel.Google Scholar - 38.Santos, F., & Carmo, J. (1996). Indirect action, influence and responsibility. In
*Proceedings of DEON, 1996*(pp. 194–215). New York: Springer-Verlag.Google Scholar - 39.Santos, F., Jones, A., & Carmo, J. (1997). Responsibility for action in organisations: A formal model. In G. Holmström-Hintikka & R. Tuomela (Eds.),
*Contemporary action theory*(Vol. 1, pp. 333–348). Dordrecht: Kluwer.Google Scholar - 40.Santos, F., & Pacheco, O. (2003). Specifying and reasoning with institutional agents. In
*Proceedings of ICAIL, 2003*(pp. 162–170). Edinburgh: ACM.Google Scholar - 41.Schmid, H. B. (2008). Plural action.
*Philosophy of the Social Sciences*,*38*(1), 25–54.CrossRefGoogle Scholar - 42.Sebastiani, R., & Tacchella, A. (2009). SAT techniques for modal and description logics. In A. Biere, M. Heule, H. Van Maaren, & T. Walsh (Eds.),
*The handbook of satisfiability*(Vol. 2, Chap. 25). Amsterdam: IOS Press.Google Scholar - 43.Segerberg, K. (1971).
*An essay in classical modal logic*. Uppsala: Filosofiska Studier, Uppsala Universitet.MATHGoogle Scholar - 44.Shapley, L. S., & Shubik, M. (1971). The assignment game I: The core.
*International Journal of Game Theory*,*1*(1), 111–130.CrossRefMATHMathSciNetGoogle Scholar - 45.Sommerhoff, G. (1969). The abstract characteristics of living systems. In F. E. Emery (Ed.),
*Systems thinking: Selected readings*. Harmonsworth: Penguin.Google Scholar - 46.Troquard, N. (2012). Coalitional agency and evidence-based ability. In
*Proceedings of AAMAS, 2012*(pp. 1245–1246). IFAAMAS.Google Scholar - 47.Troquard, N., van der Hoek, W., & Wooldridge, M. (2009). Model checking strategic equilibria. In
*Proceedings of MoChArt 2008, lecture notes in computer science*(Vol. 5348, pp. 166–188). Berlin, Heidelberg: Springer.Google Scholar - 48.Tuomela, R. (1995).
*The importance of us*. Stanford: Stanford University Press.Google Scholar - 49.Turner, J. H. (1988).
*A theory of social interaction*. Stanford, CA: Stanford University Press.Google Scholar - 50.Vardi, M. (1989). On the complexity of epistemic reasoning. In
*Proceedings of LICS, 1989*(pp. 243–252). Washington, DC: IEEE Computer Society.Google Scholar - 51.von Kutschera, F. (1986). Bewirken.
*Erkenntnis: An International Journal of Analytic Philosophy*,*24*(3), 253–281.Google Scholar - 52.Wobcke, W. (1997). Agency and the logic of ability. In
*Agents and multi-agent systems formalisms, methodologies, and applications*(pp. 31–45).Google Scholar