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Relative expressiveness of defeasible logics

Published online by Cambridge University Press:  05 September 2012

MICHAEL J. MAHER
MICHAEL J. MAHER*
Affiliation:
School of Engineering and Information TechnologyUniversity of New South Wales at the Australian Defence Forces AcademyACT 2600, Australia (e-mail: m.maher@adfa.edu.au)
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Abstract

We address the relative expressiveness of defeasible logics in the framework DL. Relative expressiveness is formulated as the ability to simulate the reasoning of one logic within another logic. We show that such simulations must be modular, in the sense that they also work if applied only to part of a theory, in order to achieve a useful notion of relative expressiveness. We present simulations showing that logics in DL with and without the capability of team defeat are equally expressive. We also show that logics that handle ambiguity differently – ambiguity blocking versus ambiguity propagating – have distinct expressiveness, with neither able to simulate the other under a different formulation of expressiveness.

Keywords

defeasible logicnon-monotonic reasoningrelative expressiveness
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 12 , Issue 4-5: 28th International Conference on Logic Programming , July 2012 , pp. 793 - 810
Copyright
Copyright © Cambridge University Press 2012

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References

Antoniou, G., Billington, D., Governatori, G. and Maher, M. J. 2000. A flexible framework for defeasible logics. In AAAI/IAAI. AAAI Press/The MIT Press, 405–410.Google Scholar
Antoniou, G., Billington, D., Governatori, G. and Maher, M. J. 2001. Representation results for defeasible logic. ACM Transactions on Computer Logic 2, 2, 255–287.CrossRefGoogle Scholar
Antoniou, G., Billington, D., Governatori, G. and Maher, M. J. 2006. Embedding defeasible logic into logic programming. TPLP 6, 6, 703–735.Google Scholar
Billington, D., Antoniou, G., Governatori, G. and Maher, M. J. 2010. An inclusion theorem for defeasible logics. ACM Transactions on Computer Logic 12, 1, 6.CrossRefGoogle Scholar
Cox, J., McAloon, K. and Tretkoff, C. 1992. Computational complexity and constraint logic programming languages. Annals of Mathematics and Artificial Intelligence 5, 2-4, 163–189.CrossRefGoogle Scholar
de Boer, F. S. and Palamidessi, C. 1991. Embedding as a tool for language comparison: On the CSP hierarchy. In CONCUR, Baeten, J. C. M. and Groote, J. F., Eds. Lecture Notes in Computer Science, vol. 527. Springer, 127–141.Google Scholar
de Boer, F. S., and Palamidessi, C. 1994. Embedding as a tool for language comparison. Information and Computation 108, 1, 128–157.CrossRefGoogle Scholar
Dix, J. 1995. A classification theory of semantics of normal logic programs: I. strong properties. Fundamenta Informaticae 22, 3, 227–255.CrossRefGoogle Scholar
Felleisen, M. 1991. On the expressive power of programming languages. Science of Computer Programming 17, 1-3, 35–75.CrossRefGoogle Scholar
Horty, J. F. 1994. Some direct theories of nonmonotonic inheritance. In Handbook of Logic in Artificial Intelligence and Logic Programming, Volume 3: Nonmonotonic Reasoning and Uncertain Reasoning. Oxford University Press, 111–187.CrossRefGoogle Scholar
Janhunen, T. 2006. Some (in)translatability results for normal logic programs and propositional theories. Journal of Applied Non-Classical Logics 16, 1-2, 35–86.CrossRefGoogle Scholar
Lam, H.-P. and Governatori, G. 2011. What are the Necessity Rules in Defeasible Reasoning? In Proceedings of the 11th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR-11), Delgrande, J. and Faber, W., Eds. Lecture Notes in Computer Science, vol. 6645. Springer Berlin/Heidelberg, Vancouver, BC, Canada, 187–192.CrossRefGoogle Scholar
Landin, P. J. 1966. The next 700 programming languages. Communication of the ACM 9, 3, 157–166.CrossRefGoogle Scholar
Maher, M. J. 2001. Propositional defeasible logic has linear complexity. TPLP 1, 6, 691–711.Google Scholar
Maher, M. J. and Governatori, G. 1999. A semantic decomposition of defeasible logics. In AAAI/IAAI. AAAI Press, 299–305.Google Scholar
Nute, D. 1994. Defeasible logic. In Handbook of Logic in Artificial Intelligence and Logic Programming, D. Gabbay, Hogger, C. and Robinson, J., Eds. Number 3. Oxford University Press, 353–395.CrossRefGoogle Scholar
Reiter, R. 1980. A logic for default reasoning. Artificial Intelligence 13, 1-2, 81–132.CrossRefGoogle Scholar
Shapiro, E. Y. 1989. The family of concurrent logic programming languages. ACM Computing Surveys 21, 3, 413–510.CrossRefGoogle Scholar
Shapiro, E. Y. 1991. Separating concurrent languages with categories of language embeddings (extended abstract). In STOC, Koutsougeras, C. and Vitter, J. S., Eds. ACM, 198–208.Google Scholar
Shoenfield, J. 1967. Mathematical Logic. Addison-Wesley.Google Scholar
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