Automated Reasoning in Deontic Logic

  • Ulrich Furbach
  • Claudia Schon
  • Frieder Stolzenburg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8875)


Deontic logic is a very well researched branch of mathematical logic and philosophy. Various kinds of deontic logics are discussed for different application domains like argumentation theory, legal reasoning, and acts in multi-agent systems. In this paper, we show how standard deontic logic can be stepwise transformed into description logic and DL-clauses, such that it can be processed by Hyper, a high performance theorem prover which uses a hypertableau calculus. Two use cases, one from multi-agent research and one from the development of normative system are investigated.


Deontic Logic Automated Theorem Proving Description Logics 


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  1. 1.
    Artosi, A., Cattabriga, P., Governatori, G.: Ked: A deontic theorem prover. In: On Legal Application of Logic Programming, ICLP 1994, pp. 60–76 (1994)Google Scholar
  2. 2.
    Baader, F., Nutt, W.: Basic description logics. In: Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F. (eds.) The Description Logic Handbook: Theory, Implementation, and Applications, pp. 43–95. Cambridge University Press (2003)Google Scholar
  3. 3.
    Bassiliades, N., Kontopoulos, E., Governatori, G., Antoniou, G.: A modal defeasible reasoner of deontic logic for the semantic web. Int. J. Semant. Web Inf. Syst. 7(1), 18–43 (2011)Google Scholar
  4. 4.
    Baumgartner, P., Furbach, U., Niemelä, I.: Hyper tableaux. In: Alferes, J.J., Pereira, L.M., Orlowska, E. (eds.) JELIA 1996. LNCS, vol. 1126, pp. 1–17. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  5. 5.
    Beirlaen, M.: Tolerating normative conflicts in deontic logic. PhD thesis, Ghent University (2012)Google Scholar
  6. 6.
    Bender, M., Pelzer, B., Schon, C.: System description: E-KRHyper 1.4 - Extensions for unique names and description logic. In: Bonacina, M.P. (ed.) CADE 2013. LNCS (LNAI), vol. 7898, pp. 126–134. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  7. 7.
    Bringsjord, S., Arkoudas, K., Bello, P.: Toward a general logicist methodology for engineering ethically correct robots. IEEE Intelligent Systems 21(4), 38–44 (2006)CrossRefGoogle Scholar
  8. 8.
    Chisolm, R.M.: Contrary-to-duty imperatives and deontic logic. Analysis 23, 33–36 (1963)CrossRefGoogle Scholar
  9. 9.
    Furbach, U., Schon, C.: Deontic logic for human reasoning. CoRR, abs/1404.6974 (2014)Google Scholar
  10. 10.
    Gabbay, D., Horty, J., Parent, X., van der Meyden, R., van der Torre, L. (eds.): Handbook of Deontic Logic and Normative Systems. College Publications (2013)Google Scholar
  11. 11.
    Horty, J.F.: Agency and Deontic Logic. Oxford University Press, Oxford (2001)CrossRefzbMATHGoogle Scholar
  12. 12.
    Klarman, S., Gutiérrez-Basulto, V.: Description logics of context. Journal of Logic and Computation (2013)Google Scholar
  13. 13.
    McNamara, P.: Deontic logic. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. Stanford University (2010)Google Scholar
  14. 14.
    McNamara, P., Prakken, H.: Norms, Logics and Information Systems: New Studies in Deontic Logic and Computer Science. Frontiers in artificial intelligence and applications. IOS Press (1999)Google Scholar
  15. 15.
    Motik, B., Shearer, R., Horrocks, I.: Optimized Reasoning in Description Logics using Hypertableaux. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 67–83. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Murakami, Y.: Utilitarian deontic logic. In: Proceedings of the Fifth International Conference on Advances in Modal Logic (AiML 2004), pp. 288–302 (2004)Google Scholar
  17. 17.
    Plaisted, D.A., Greenbaum, S.: A structure-preserving clause form translation. J. Symb. Comput. 2(3), 293–304 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Schild, K.: A correspondence theory for terminological logics: Preliminary report. In: Proc. of IJCAI 1991, pp. 466–471 (1991)Google Scholar
  19. 19.
    Schmidt, R.A., Hustadt, U.: First-order resolution methods for modal logics. In: Voronkov, A., Weidenbach, C. (eds.) Programming Logics. LNCS, vol. 7797, pp. 345–391. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  20. 20.
    Sirin, E., Parsia, B., Grau, B.C., Kalyanpur, A., Katz, Y.: Pellet: A practical OWL-DL reasoner. Web Semantics: Science, Services and Agents on the World Wide Web 5(2), 51–53 (2007)CrossRefGoogle Scholar
  21. 21.
    von Kutschera, F.: Einführung in die Logik der Normen, Werte und Entscheidungen. Alber (1973)Google Scholar
  22. 22.
    Pelzer, B., Wernhard, C.: System description: E- KRHyper. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 508–513. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ulrich Furbach
    • 1
  • Claudia Schon
    • 1
  • Frieder Stolzenburg
    • 2
  1. 1.Universität Koblenz-LandauKoblenzGermany
  2. 2.Harz University of Applied SciencesWernigerodeGermany

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