A Deontic Logic Reasoning Infrastructure

  • Christoph BenzmüllerEmail author
  • Xavier Parent
  • Leendert van der Torre
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10936)


A flexible infrastructure for the automation of deontic and normative reasoning is presented. Our motivation is the development, study and provision of legal and moral reasoning competencies in future intelligent machines. Since there is no consensus on the “best” deontic logic formalisms and since the answer may be application specific, a flexible infrastructure is proposed in which candidate logic formalisms can be varied, assessed and compared in experimental ethics application studies. Our work thus links the historically rich research areas of classical higher-order logic, deontic logics, normative reasoning and formal ethics.


  1. 1.
    Anderson, M., Anderson, S.L.: Toward ensuring ethical behavior from autonomous systems: a case-supported principle-based paradigm. Ind. Robot 42(4), 324–331 (2015)CrossRefGoogle Scholar
  2. 2.
    Andrews, P.: Church’s type theory. In: Zalta, E. (ed.) The Stanford Encyclopedia of Philosophy, Spring 2014 edn (2014)Google Scholar
  3. 3.
    Åqvist, L.: Deontic logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn, vol. 8, pp. 147–264. Kluwer Academic Publishers, Dordrecht, Holland (2002)CrossRefGoogle Scholar
  4. 4.
    Benzmüller, C.: Cut-elimination for quantified conditional logic. J. Philos. Logic 46(3), 333–353 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Benzmüller, C.: Recent successes with a meta-logical approach to universal logical reasoning (extended abstract). In: da Costa Cavalheiro, S.A., Fiadeiro, J.L. (eds.) SBMF 2017. LNCS, vol. 10623, pp. 7–11. Springer, Cham (2017). Scholar
  6. 6.
    Benzmüller, C., Farjami, A., Parent, X.: Faithful semantical embedding of a dyadic deontic logic in HOL. Technical report, CoRR (2018).
  7. 7.
    Benzmüller, C., Miller, D.: Automation of higher-order logic. In: Gabbay, D.M., Siekmann, J.H., Woods, J. (eds.) Handbook of the History of Logic. Computational Logic, vol. 9, pp. 215–254. North Holland, Elsevier (2014)CrossRefGoogle Scholar
  8. 8.
    Benzmüller, C., Parent, X.: First experiments with a flexible infrastructure for normative reasoning. Technical report, CoRR (2018).
  9. 9.
    Benzmüller, C., Parent, X.: I/O logic in HOL – first steps. Technical report, CoRR (2018).
  10. 10.
    Benzmüller, C., Paulson, L.: Quantified multimodal logics in simple type theory. Log. Univers. 7(1), 7–20 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Benzmüller, C., Sultana, N., Paulson, L.C., Theiß, F.: The higher-order prover LEO-II. J. Autom. Reason. 55(4), 389–404 (2015)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Benzmüller, C., Weber, L., Woltzenlogel Paleo, B.: Computer-assisted analysis of the Anderson-Hájek controversy. Log. Univers. 11(1), 139–151 (2017)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Benzmüller, C., Woltzenlogel Paleo, B.: The inconsistency in Gödel’s ontological argument: a success story for AI in metaphysics. In: Kambhampati, S. (ed.) IJCAI 2016, vol. 1–3, pp. 936–942. AAAI Press (2016)Google Scholar
  14. 14.
    Blanchette, J.C., Nipkow, T.: Nitpick: a counterexample generator for higher-order logic based on a relational model finder. In: Kaufmann, M., Paulson, L.C. (eds.) ITP 2010. LNCS, vol. 6172, pp. 131–146. Springer, Heidelberg (2010). Scholar
  15. 15.
    Blanchette, J.C., Böhme, S., Paulson, L.C.: Extending Sledgehammer with SMT solvers. J. Autom. Reason. 51(1), 109–128 (2013)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Blanchette, J.C., Popescu, A., Wand, D., Weidenbach, C.: More SPASS with Isabelle - superposition with hard sorts and configurable simplification. In: Beringer, L., Felty, A. (eds.) ITP 2012. LNCS, vol. 7406, pp. 345–360. Springer, Heidelberg (2012). Scholar
  17. 17.
    Bringsjord, S., Arkoudas, K., Bello, P.: Toward a general logicist methodology for engineering ethically correct robots. IEEE Intell. Syst. 21, 38–44 (2006)CrossRefGoogle Scholar
  18. 18.
    Carmo, J., Jones, A.J.I.: Deontic logic and contrary-to-duties. In: Gabbay, D.M., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 8, pp. 265–343. Springer, Dordrecht (2002). Scholar
  19. 19.
    Carmo, J., Jones, A.J.I.: Completeness and decidability results for a logic of contrary-to-duty conditionals. J. Logic Comput. 23(3), 585–626 (2013)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Dennis, L.A., Fischer, M.: Practical challenges in explicit ethical machine reasoning. In: ISAIM 2018, Fort Lauderdale, Florida, USA (2018)Google Scholar
  21. 21.
    Dennis, L.A., Fisher, M., Slavkovik, M., Webster, M.: Formal verification of ethical choices in autonomous systems. Rob. Auton. Syst. 77, 1–14 (2016)CrossRefGoogle Scholar
  22. 22.
    Deters, M., Reynolds, A., King, T., Barrett, C.W., Tinelli, C.: A tour of CVC4: how it works, and how to use it. In: Formal Methods in Computer-Aided Design, FMCAD 2014, Lausanne, Switzerland, 21–24 October 2014, p. 7. IEEE (2014)Google Scholar
  23. 23.
    Dignum, V.: Responsible autonomy. In: IJCAI 2017, pp. 4698–4704 (2017)Google Scholar
  24. 24.
    Furbach, U., Schon, C., Stolzenburg, F.: Automated reasoning in deontic logic. In: Murty, M.N., He, X., Chillarige, R.R., Weng, P. (eds.) MIWAI 2014. LNCS (LNAI), vol. 8875, pp. 57–68. Springer, Cham (2014). Scholar
  25. 25.
    Gabbay, D., Horty, J., Parent, X., van der Meyden, R., van der Torre, L. (eds.): Handbook of Deontic Logic and Normative Systems. College Publications, London (2013)Google Scholar
  26. 26.
    Gordon, T.: The Pleading Game: An Artificial Intelligence Model of Procedural Approach. Springer, New York (1995)CrossRefGoogle Scholar
  27. 27.
    Hansen, J.: Reasoning about permission and obligation. In: Hansson, S.O. (ed.) David Makinson on Classical Methods for Non-Classical Problems. OCL, vol. 3, pp. 287–333. Springer, Dordrecht (2014). Scholar
  28. 28.
    Hansson, B.: An analysis of some deontic logics. No\(\hat{\text{u}}\)s 3(4), 373–398 (1969)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Horty, J.: Agency and Deontic Logic. OUP, London (2009)Google Scholar
  30. 30.
    Kirchner, D., Benzmüller, C., Zalta, E.N.: Mechanizing principia logico-metaphysica in functional type theory. CoRR (2017).
  31. 31.
    Makinson, D., van der Torre, L.W.N.: Input/output logics. J. Philos. Logic 29(4), 383–408 (2000)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Nipkow, T., Paulson, L., Wenzel, M.: Isabelle/HOL: A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002). Scholar
  33. 33.
    Parent, X.: Completeness of Åqvist’s systems E and F. Rev. Symb. Logic 8(1), 164–177 (2015)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Parent, X., van der Torre, L.: Input/output logic. In: Gabbay et al. [25], pp. 499–544 (2013)Google Scholar
  35. 35.
    Parent, X., van der Torre, L.: Detachment in normative systems: examples, inference patterns, properties. IfCoLog J. Logics Appl. 4(9), 2295–3039 (2017)Google Scholar
  36. 36.
    Parent, X., van der Torre, L.: The pragmatic oddity in a norm-based semantics. In: Governatori, G. (ed.) ICAIL 2017, Proceedings, pp. 169–178. ACM, New York (2017)Google Scholar
  37. 37.
    Pereira, L.M., Saptawijaya, A.: Programming Machine Ethics. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol. 26. Springer, Cham (2016). Scholar
  38. 38.
    Sartor, G.: Legal Reasoning: A Cognitive Approach to Law. Springer, Dordrecht (2005)Google Scholar
  39. 39.
    von Wright, G.H.: Deontic logic. Mind 60, 1–15 (1951)CrossRefGoogle Scholar
  40. 40.
    Zalta, E.N.: Principia logico-metaphysica. Draft version (2016).

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Christoph Benzmüller
    • 1
    Email author
  • Xavier Parent
    • 1
  • Leendert van der Torre
    • 1
  1. 1.Computer Science and CommunicationsUniversity of LuxembourgEsch-sur-AlzetteLuxembourg

Personalised recommendations