A Decidable Multi-agent Logic for Reasoning About Actions, Instruments, and Norms

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12061)


We formally introduce a novel, yet ubiquitous, category of norms: norms of instrumentality. Norms of this category describe which actions are obligatory, or prohibited, as instruments for certain purposes. We propose the Logic of Agency and Norms (\(\mathsf {LAN}\)) that enables reasoning about actions, instrumentality, and normative principles in a multi-agent setting. Leveraging \(\mathsf {LAN}\), we formalize norms of instrumentality and compare them to two prevalent norm categories: norms to be and norms to do. Last, we pose principles relating the three categories and evaluate their validity vis-à-vis notions of deliberative acting. On a technical note, the logic will be shown decidable via the finite model property.


Agency logic Action constants Action logic Andersonian reduction Decidability Deontic logic Norms of instrumentality 



Work funded by projects: FWF I2982, FWF W1255-N23, FWF Y544-N2, and WWTF MA16-028.


  1. 1.
    d’Altan, P., Meyer, J.J., Wieringa, R.J.: An integrated framework for ought-to-be and ought-to-do constraints. Artif. Intell. Law 4(2), 77–111 (1996)CrossRefGoogle Scholar
  2. 2.
    Anderson, A.R., Moore, O.K.: The formal analysis of normative concepts. Am. Sociol. Rev. 22(1), 9–17 (1957)CrossRefGoogle Scholar
  3. 3.
    Belnap, N., Perloff, M., Xu, M.: Facing the Future. Agents and Choices in our Indeterminist World. Oxford University Press, Oxford (2001)Google Scholar
  4. 4.
    van Berkel, K., Pascucci, M.: Notions of instrumentality in agency logic. In: Miller, T., Oren, N., Sakurai, Y., Noda, I., Savarimuthu, B.T.R., Cao Son, T. (eds.) PRIMA 2018. LNCS (LNAI), vol. 11224, pp. 403–419. Springer, Cham (2018). Scholar
  5. 5.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)CrossRefGoogle Scholar
  6. 6.
    Broersen, J.: Deontic epistemic stit logic distinguishing modes of mens rea. J. Appl. Logic 9(2), 137–152 (2011)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Brown, M.A.: On the logic of ability. J. Philos. Logic 17(1), 1–26 (1988)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Castañeda, H.N.: On the semantics of the ought-to-do. In: Davidson, D., Harman, G. (eds.) Semantics of Natural Language. Synthese Library, vol. 40, pp. 675–694. Springer, Dordrecht (1972). Scholar
  9. 9.
    Chisholm, R.: Contrary-to-duty imperatives and deontic logic. Analysis 24, 33–36 (1963)CrossRefGoogle Scholar
  10. 10.
    Fischer, M., Ladner, R.: Propositional dynamic logic of regular programs. J. Comput. Syst. Sci. 18(2), 194–211 (1979)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Governatori, G.: Practical normative reasoning with defeasible deontic logic. In: d’Amato, C., Theobald, M. (eds.) Reasoning Web 2018. LNCS, vol. 11078, pp. 1–25. Springer, Cham (2018). Scholar
  12. 12.
    Governatori, G., Hashmi, M.: No time for compliance. In: 19th International Enterprise Distributed Object Computing Conference, pp. 9–18. IEEE (2015)Google Scholar
  13. 13.
    Governatori, G., Olivieri, F., Rotolo, A., Scannapieco, S.: Computing strong and weak permissions in defeasible logic. J. Philos. Logic 42(6), 799–829 (2013). Scholar
  14. 14.
    Hansson, S.O.: The varieties of permission. In: Gabbay, D., Horty, J., Parent, X., van der Meyden, R., van der Torre, L. (eds.) Handbook of Deontic Logic and Normative Systems, pp. 195–240. College Publications, London (2013)Google Scholar
  15. 15.
    Horty, J.: Agency and Deontic Logic. Oxford University Press, Oxford (2001)CrossRefGoogle Scholar
  16. 16.
    Kant, I.: Critique of Pure Reason. Cambridge University Press, Cambridge (2000)Google Scholar
  17. 17.
    Meyer, J.J.C.: A different approach to deontic logic: deontic logic viewed as a variant of dynamic logic. Notre Dame J. Formal Logic 29(1), 109–136 (1988)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Pascucci, M.: Anderson’s restriction of deontic modalities to contingent propositions. Theoria 83(4), 440–470 (2017)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Prakken, H., Sergot, M.: Dyadic deontic logic and contrary-to-duty obligations. In: Nute, D. (ed.) Defeasible Deontic Logic, pp. 223–262. Springer, Dordrecht (1997). Scholar
  20. 20.
    Prisacariu, C., Schneider, G.: A dynamic deontic logic for complex contracts. J. Logic Algebraic Program. 81(4), 458–490 (2012)MathSciNetCrossRefGoogle Scholar
  21. 21.
    von Wright, G.H.: Deontic logic. Mind 60(237), 1–15 (1951)CrossRefGoogle Scholar
  22. 22.
    von Wright, G.H.: An Essay in Deontic Logic and the General Theory of Action. North Holland Publishing Company, Amsterdam (1968)zbMATHGoogle Scholar
  23. 23.
    von Wright, G.H.: The Varieties of Goodness. Routledge & Kegan Paul, London and Henley (1972). fourth impressionGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institut für Logic and ComputationTU WienViennaAustria
  2. 2.BrisbaneAustralia

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