skip to main content
research-article

An inclusion theorem for defeasible logics

Published:26 November 2010Publication History
Skip Abstract Section

Abstract

Defeasible reasoning is a computationally simple nonmonotonic reasoning approach that has attracted significant theoretical and practical attention. It comprises a family of logics that capture different intuitions, among them ambiguity propagation versus ambiguity blocking, and the adoption or rejection of team defeat. This article provides a compact presentation of the defeasible logic variants, and derives an inclusion theorem which shows that different notions of provability in defeasible logic form a chain of levels of proof.

References

  1. Antoniou, G. and Bikakis, A. 2007. DR-Prolog: A system for defeasible reasoning with rules and ontologies on the semantic web. IEEE Trans. Knowl. Data Eng. 19 2, 233--245. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Antoniou, G., Billington, D., Governatori, G., and Maher, M. J. 2000a. A flexible framework for defeasible logics. In Proceedings of the 17th National Conference on Artificial Intelligence and 12th Conference on on Innovative Applications of Artificial Intelligence (AAAI/IAAI), Menlo Park, CA/MIT Press, Cambridge, MA, 405--410. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. Antoniou, G., Billington, D., Governatori, G., and Maher, M. J. 2001. Representation results for defeasible logic. ACM Trans. Comput. Log. 2, 2, 255--287. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Antoniou, G., Billington, D., Governatori, G., and Maher, M. J. 2006. Embedding defeasible logic into logic programming. Theor. Pract. Log. Program. 6, 6, 703--735. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Antoniou, G., Billington, D., Governatori, G., Maher, M. J., and Rock, A. 2000b. A family of defeasible reasoning logics and its implementation. In Proceedings of the 14th European Conference on Artificial Intelligence (ECAI), W. Horn, Ed. IOS Press, Amsterdam, The Netherlands, 459--463.Google ScholarGoogle Scholar
  6. Antoniou, G., Maher, M. J., and Billington, D. 2000c. Defeasible logic versus logic programming without negation as failure. J. Log. Program. 42, 1, 47--57.Google ScholarGoogle ScholarCross RefCross Ref
  7. Balduccini, M. and Gelfod, M. 2003. Logic programs with consistency-restoring rules. In Proceedings of the International Symposium on Logical Formalization of Commonsense Reasoning. P. Doherty, J. McCarthy, and M.-A. Williams, Eds. AAAI Spring Symposium Series. AAAI, Press, Menlo Park, CA, 9--18.Google ScholarGoogle Scholar
  8. Bassiliades, N., Antoniou, G., and Vlahavas, I. P. 2006. A defeasible logic reasoner for the semantic Web. Int. J. Semant. Web Inform. Syst. 2, 1, 1--41.Google ScholarGoogle ScholarCross RefCross Ref
  9. Billington, D. 1993. Defeasible logic is stable. J. Log. Comput. 3, 4, 379--400.Google ScholarGoogle ScholarCross RefCross Ref
  10. Bochman, A. 2003. Collective argumentation and disjunctive logic programming. J. Log. Comput. 13, 3, 405--428.Google ScholarGoogle ScholarCross RefCross Ref
  11. Buccafurri, F., Leone, N., and Rullo, P. 1997. Strong and weak constraints in disjunctive datalog. In Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR), J. Dix, U. Furbach, and A. Nerode, Eds. Lecture Notes in Computer Science, vol. 1265. Springer, Berlin, Germany, 2--17. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Dimopoulos, Y. and Kakas, A. C. 1995. Logic programming without negation as failure. In Proceedings of the International Symposium on Logic Programming. MIT Press, Cambridge, MA, 369--383.Google ScholarGoogle Scholar
  13. Dumas, M., Governatori, G., ter Hofstede, A. H. M., and Oaks, P. 2002. A formal approach to negotiating agents development. Electron. Com. Res. Appl. 1, 2, 193--207.Google ScholarGoogle ScholarCross RefCross Ref
  14. Dung, P. M. 1995. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Art. Intell. 77, 2, 321--358. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Dung, P. M., Mancarella, P., and Toni, F. 2007. Computing ideal sceptical argumentation. Art. Intell. 171, 10-15, 642--674. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. Eriksson Lundström, J., Governatori, G., Thakur, S., and Padmanabhan, V. 2007. An asymmetric protocol for argumentation games in defeasible logic. In Proceedings of the 10th Pacific Rim International Conference on Multi-Agents (PRIMA), A. K. Ghose, G. Governatori, and R. Sadananda, Eds. Lecture Notes in Computer Science, vol. 5044. Springer, Berlin, Germany, 219--231. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Governatori, G. 2005. Representing business contracts in RuleML. Int. J. Coop. Inform. Syst. 14, 2-3, 181--216.Google ScholarGoogle ScholarCross RefCross Ref
  18. Governatori, G. and Maher, M. J. 2000. An argumentation-theoretic characterization of defeasible logic. In Proceedings of the 14th European Conference on Artificial Intelligence (ECAI). W. Horn, Ed. IOS Press, Amsterdam, The Netherlands, 469--473.Google ScholarGoogle Scholar
  19. Governatori, G., Maher, M. J., Billington, D., and Antoniou, G. 2004. Argumentation semantics for defeasible logics. J. Log. Comput. 14, 5, 675--702. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Governatori, G. and Rotolo, A. 2008. BIO logical agents: Norms, beliefs, intentions in defeasible logic. Auton. Agents Multi-Agent Syst. 17, 1, 36--69. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. Governatori, G., Rotolo, A., and Padmanabhan, V. 2006. The cost of social agents. In Proceedings of the 5th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS). H. Nakashima, M. P. Wellman, G. Weiss, and P. Stone, Eds. 513--520. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Governatori, G., Rotolo, A., and Sartor, G. 2005. Temporalised normative positions in defeasible logic. In Proceedings of the 10th International Conference on Artificial Intelligence and Law (ICAIL). ACM Press, New York, NY, 25--34. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. Govindarajan, K., Jayaraman, B., and Mantha, S. 1995. Preference logic programming. In Proceedings of the 12th International Conference on Logic Programming. MIT Press, Cambridge, MA, 731--745.Google ScholarGoogle Scholar
  24. Grosof, B. N. 1997. Prioritized conflict handling for logic programs. In Proceedings of the 1997 International Logic Programming Symposium. MIT Press, Cambridge, MA, 197--211. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Grosof, B. N., Labrou, Y., and Chan, H. Y. 1999. A declarative approach to business rules in contracts: Courteous logic programs in xml. In Proceedings of the ACM Conference on Electronic Commerce. 68--77. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Horty, J. F. 2001. Argument construction and reinstatement in logics for defeasible reasoning. Art. Intell. Law 9, 1, 1--28.Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. Horty, J. F. 2002. Skepticism and floating conclusions. Art. Intell. 135, 1-2, 55--72. Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. Horty, J. F. 2007. Defaults with priorities. J. Phil. Log. 36, 367--413.Google ScholarGoogle ScholarCross RefCross Ref
  29. Kraus, S., Lehmann, D. J., and Magidor, M. 1990. Nonmonotonic reasoning, preferential models and cumulative logics. Art. Intell. 44, 1-2, 167--207. Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. Kunen, K. 1987. Negation in logic programming. J. Log. Program. 4, 4, 289--308. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. Maher, M. J. 2001. Propositional defeasible logic has linear complexity. Theor. Pract. Log. Program. 1, 6, 691--711. Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. Maher, M. J. 2002. A model-theoretic semantics for defeasible logic. In Proceedings of the Workshop on Paraconsistent Computational Logic. 67--80.Google ScholarGoogle Scholar
  33. Maher, M. J. and Governatori, G. 1999. A semantic decomposition of defeasible logics. In Proceedings of the 16th National Conference on Artificial Intelligence and 11th Conference on Innovative Applications of Artificial Intelligence (AAAI/IAAI). 299--305. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. Makinson, D. 1994. General patterns in nonmonotonic reasoning. In Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. II, D. Gabbay, Ed. Oxford University Press, Oxford, U.K., 35--110. Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. McCarthy, J. 1980. Circumscription—a form of non-monotonic reasoning. Art. Intell. 13, 1-2, 27--39.Google ScholarGoogle ScholarDigital LibraryDigital Library
  36. Moore, R. C. 1985. Semantical considerations on nonmonotonic logic. Art. Intell. 25, 1, 75--94. Google ScholarGoogle ScholarDigital LibraryDigital Library
  37. Nielsen, S. H. and Parsons, S. 2006. A generalization of dung's abstract framework for argumentation: Arguing with sets of attacking arguments. In Proceedings of the 3rd International Workshop on Argumentation in Multi-Agent Systems (ArgMAS), N. Maudet, S. Parsons, and I. Rahwan, Eds. Lecture Notes in Computer Science, vol. 4766. Springer, Berlin, Germany, 54--73.Google ScholarGoogle Scholar
  38. Nute, D. 1997. Defeasible logic. In Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. III. D. Gabbay, Ed. Oxford University Press, Oxford, U.K., 353--395. Google ScholarGoogle ScholarDigital LibraryDigital Library
  39. Prakken, H. 1997. Logical Tools for Modelling Legal Argument: A Study of Defeasible Reasoning in Law. Kluwer Academic Publishers, Dordrecht, The Netherlands. Google ScholarGoogle ScholarDigital LibraryDigital Library
  40. Prakken, H. 2005. A study of accrual of arguments, with applications to evidential reasoning. In Proceedings of the 10th International Conference on Artificial Intelligence and Law (ICAIL). ACM Press, New York, NY, 85--94. Google ScholarGoogle ScholarDigital LibraryDigital Library
  41. Prakken, H. and Sartor, G. 2007. Formalising arguments about the burden of persuasion. In Proceedings of the 11th International Conference on Artificial Intelligence and Law (ICAIL). 97--106. Google ScholarGoogle ScholarDigital LibraryDigital Library
  42. Reeves, D. M., Wellman, M. P., and Grosof, B. N. 2002. Automated negotiation from declarative contract descriptions. Comput. Intell. 18, 4, 482--500.Google ScholarGoogle ScholarCross RefCross Ref
  43. Reiter, R. 1980. A logic for default reasoning. Art. Intell. 13, 1-2, 81--132.Google ScholarGoogle ScholarDigital LibraryDigital Library
  44. Stein, L. A. 1992. Resolving ambiguity in nonmonotonic inheritance hierarchies. Art. Intell. 55, 2, 259--310. Google ScholarGoogle ScholarDigital LibraryDigital Library
  45. Touretzky, D. S., Horty, J. F., and Thomason, R. H. 1987. A clash of intuitions: The current state of nonmonotonic multiple inheritance systems. In Proceedings of IJCAI. 476--482. Google ScholarGoogle ScholarDigital LibraryDigital Library
  46. Wang, X., You, J.-H., and Yuan, L.-Y. 1996. Nonmonotonic reasoning by monotonic inference with priority constraints. In Non-Monotonic Extensions of Logic Programming (NMELP), J. Dix, L. M. Pereira, and T. C. Przymusinski, Eds. Lecture Notes in Computer Science, vol. 1216. Springer, Berlin, Germany, 91--109. Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. An inclusion theorem for defeasible logics

      Recommendations

      Comments

      Login options

      Check if you have access through your login credentials or your institution to get full access on this article.

      Sign in

      Full Access

      • Published in

        cover image ACM Transactions on Computational Logic
        ACM Transactions on Computational Logic  Volume 12, Issue 1
        October 2010
        334 pages
        ISSN:1529-3785
        EISSN:1557-945X
        DOI:10.1145/1838552
        Issue’s Table of Contents

        Copyright © 2010 ACM

        Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

        Publisher

        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 26 November 2010
        • Accepted: 1 June 2009
        • Revised: 1 January 2009
        • Received: 1 March 2008
        Published in tocl Volume 12, Issue 1

        Permissions

        Request permissions about this article.

        Request Permissions

        Check for updates

        Qualifiers

        • research-article
        • Research
        • Refereed

      PDF Format

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader