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Relative Expressiveness of Well-Founded Defeasible Logics

  • Michael J. Maher
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8272)

Abstract

An approach to formulating relative expressiveness of defeasible logics was introduced in [14]. In this paper we address the relative expressiveness of the well-founded defeasible logics in the framework WFDL and their relationship to the defeasible logics in the framework DL. We show that, in terms of defeasible reasoning, the logics in WFDL have greater (or equal) expressiveness than those in DL, but it is not clear whether they have strictly greater expressiveness. We also show that different treatments of ambiguity lead to different expressiveness in WFDL, as it does in DL.

Keywords

Logic Program Inference Rule Logic Programming Strict Rule Superiority Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Antoniou, G., Billington, D., Governatori, G., Maher, M.J.: On the modelling and analysis of regulations. In: Proc. Australasian Conf. on Information Systems, pp. 20–29 (1999)Google Scholar
  2. 2.
    Antoniou, G., Billington, D., Governatori, G., Maher, M.J.: Representation results for defeasible logic. ACM Trans. Comput. Log. 2(2), 255–287 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Antoniou, G., Billington, D., Governatori, G., Maher, M.J.: Embedding defeasible logic into logic programming. TPLP 6(6), 703–735 (2006)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Bassiliades, N., Antoniou, G., Vlahavas, I.P.: A defeasible logic reasoner for the semantic web. Int. J. Semantic Web Inf. Syst. 2(1), 1–41 (2006)CrossRefGoogle Scholar
  5. 5.
    Billington, D., Antoniou, G., Governatori, G., Maher, M.J.: An inclusion theorem for defeasible logics. ACM Trans. Comput. 12(1), 6 (2010)MathSciNetGoogle Scholar
  6. 6.
    Dumas, M., Governatori, G., ter Hofstede, A.H.M., Oaks, P.: A formal approach to negotiating agents development. Electronic Commerce Research and Applications 1(2), 193–207 (2002)CrossRefGoogle Scholar
  7. 7.
    Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell. 77(2), 321–358 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Gelder, A.V., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. J. ACM 38(3), 620–650 (1991)zbMATHGoogle Scholar
  9. 9.
    Governatori, G.: Representing business contracts in ruleml. Int. J. Cooperative Inf. Syst. 14(2-3), 181–216 (2005)CrossRefGoogle Scholar
  10. 10.
    Governatori, G., Rotolo, A.: Changing legal systems: legal abrogations and annulments in defeasible logic. Logic Journal of the IGPL 18(1), 157–194 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Governatori, G., Rotolo, A., Padmanabhan, V.: The cost of social agents. In: Nakashima, H., Wellman, M.P., Weiss, G., Stone, P. (eds.) AAMAS, pp. 513–520. ACM (2006)Google Scholar
  12. 12.
    Grosof, B.N.: Prioritized conflict handling for logic programs. In: ILPS, pp. 197–211 (1997)Google Scholar
  13. 13.
    Grosof, B.N., Labrou, Y., Chan, H.Y.: A declarative approach to business rules in contracts: courteous logic programs in XML. In: ACM Conference on Electronic Commerce, pp. 68–77 (1999)Google Scholar
  14. 14.
    Maher, M.J.: Relative expressiveness of defeasible logics. TPLP 12(4-5), 793–810 (2012)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Maher, M.J.: Relative expressiveness of defeasible logics II. TPLP 13(4-5), 579–592 (2013)Google Scholar
  16. 16.
    Maher, M.J., Governatori, G.: A semantic decomposition of defeasible logics. In: AAAI/IAAI, pp. 299–305. AAAI Press (1999)Google Scholar
  17. 17.
    Maier, F., Nute, D.: Ambiguity propagating defeasible logic and the well-founded semantics. In: Fisher, M., van der Hoek, W., Konev, B., Lisitsa, A. (eds.) JELIA 2006. LNCS (LNAI), vol. 4160, pp. 306–318. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  18. 18.
    Maier, F., Nute, D.: Well-founded semantics for defeasible logic. Synthese 176(2), 243–274 (2010)CrossRefzbMATHGoogle Scholar
  19. 19.
    Nute, D.: Defeasible logic. In: Bartenstein, O., Geske, U., Hannebauer, M., Yoshie, O. (eds.) INAP 2001. LNCS (LNAI), vol. 2543, pp. 151–169. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  20. 20.
    Prakken, H.: Logical Tools for Modelling Legal Argument: A Study of Defeasible Reasoning in Law. Kluwer (1997)Google Scholar
  21. 21.
    Rahwan, I., Simari, G.: Argumentation in Artificial Intelligence. Springer (2009)Google Scholar
  22. 22.
    Reeves, D.M., Wellman, M.P., Grosof, B.N.: Automated negotiation from declarative contract descriptions. Computational Intelligence 18(4), 482–500 (2002)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Michael J. Maher
    • 1
  1. 1.School of Engineering and Information TechnologyThe University of New South WalesCanberraAustralia

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