Ambiguity Propagating Defeasible Logic and the Well-Founded Semantics

  • Frederick Maier
  • Donald Nute
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4160)


The most recent version of defeasible logic (Nute, 1997) is related to the well-founded semantics by translating defeasible theories into normal logic programs using a simple scheme proposed in (Brewka, 2001). It is found that by introducing ambiguity propagation into this logic, the assertions of defeasible theories coincide with the well-founded models of their logic program translations. Without this addition, the two formalisms are found to disagree in important cases.

A translation in the other direction is also provided. By treating default negated atoms as presumptions in defeasible logic, normal logic programs can be converted into equivalent defeasible theories.


Logic Program Proof Theory Strict Rule Default Theory Proof Tree 
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  1. Antoniou, G., Maher, M.J.: Embedding defeasible logic into logic programs. In: Stuckey, P.J. (ed.) ICLP 2002. LNCS, vol. 2401, pp. 393–404. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. Antoniou, G., Billington, D., Governatori, G., Maher, M.J., Rock, A.: A family of defeasible reasoning logics and its implementation. In: ECAI, pp. 459–463 (2000)Google Scholar
  3. Brewka, G.: On the relationship between defeasible logic and well-founded semantics. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS, vol. 2173, pp. 121–132. Springer, Heidelberg (2001)Google Scholar
  4. Emden, M.H.V., Kowalski, R.: The semantics of predicate logic as a programming language. Journal of the ACM 23, 733–742 (1976)MATHCrossRefGoogle Scholar
  5. Gelder, A.V., Ross, K.A., Schlipf, J.: Unfounded sets and well-founded semantics for general logic programs. In: Proceedings 7th ACM Symposium on Principles of Database Systems, pp. 221–230 (1988)Google Scholar
  6. Gelder, A.V., Ross, K.A., Schlipf, J.: The well-founded semantics for general logic programs. Journal of the ACM, 221–223 (1991)Google Scholar
  7. Kunen, K.: Negation in logic programming. Journal of Logic Programming 4, 289–308 (1987)MATHCrossRefMathSciNetGoogle Scholar
  8. Maier, F., Nute, D.: Relating defeasible logic to the well-founded semantics for normal logic programs. In: Delgrande, J.P., Schaub, T. (eds.) NMR (2006)Google Scholar
  9. Makinson, D., Schechta, K.: Floating conclusions and zombie paths: two deep difficulties in the ’directly skeptical’ approach to inheritance nets. Artificial Intelligence 48, 199–209 (1991)MATHCrossRefMathSciNetGoogle Scholar
  10. Nute, D.: Basic defeasible logic. In: del Cerro, L.F., Penttonen, M. (eds.) Intensional Logics for Programming, pp. 125–154. Oxford University Press, Oxford (1992)Google Scholar
  11. Nute, D.: Defeasible logic. In: Gabbay, D., Hogger, C. (eds.) Handbook of Logic for Artificial Intelligence and Logic Programming, vol. III, pp. 353–395. Oxford University Press, Oxford (1994)Google Scholar
  12. Nute, D.: Apparent obligation. In: Nute, D. (ed.) Defeasible Deontic Logic. Synthese Library, pp. 287–315. Kluwer Academic Publishers, Dordrecht (1997)Google Scholar
  13. Nute, D.: Defeasible logic: Theory, implementation, and applications. In: Bartenstein, O., Geske, U., Hannebauer, M., Yoshie, O. (eds.) INAP 2001. LNCS, vol. 2543, pp. 87–114. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. Reiter, R.: A logic for default reasoning. Artificial Intelligence 13, 81–132 (1980)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Frederick Maier
    • 1
  • Donald Nute
    • 1
  1. 1.Department of Computer Science and Artificial Intelligence CenterThe University of GeorgiaAthensUSA

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