Automated Reasoning in Deontic Logic

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

Abstract

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.

Keywords

Deontic Logic Automated Theorem Proving Description Logics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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)CrossRefMATHGoogle 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)CrossRefMATHMathSciNetGoogle 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

Personalised recommendations