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Annotated defeasible logic

Published online by Cambridge University Press:  22 August 2017

GUIDO GOVERNATORI  and
MICHAEL J. MAHER
GUIDO GOVERNATORI
Affiliation:
Data61, CSIRO, Australia, Brisbane (e-mail: [email protected])
MICHAEL J. MAHER
Affiliation:
Reasoning Research Institute, Australia, Canberra (e-mail: [email protected])
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Abstract

Defeasible logics provide several linguistic features to support the expression of defeasible knowledge. There is also a wide variety of such logics, expressing different intuitions about defeasible reasoning. However, the logics can only combine in trivial ways. This limits their usefulness in contexts where different intuitions are at play in different aspects of a problem. In particular, in some legal settings, different actors have different burdens of proof, which might be expressed as reasoning in different defeasible logics. In this paper, we introduce annotated defeasible logic as a flexible formalism permitting multiple forms of defeasibility, and establish some properties of the formalism.

Keywords

defeasible logicnon-monotonic reasoningannotated logicslegal reasoning
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 17 , Special Issue 5-6: 33rd International Conference on Logic Programming , September 2017 , pp. 819 - 836
Copyright
Copyright © Cambridge University Press 2017 

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References

Antoniou, G., Billington, D., Governatori, G. and Maher, M. J. 2000. A flexible framework for defeasible logics. In Proc. of AAAI National Conference on Artificial Intelligence. AAAI Press/The MIT Press, 405–410.Google Scholar
Antoniou, G., Maher, M. J. and Billington, D. 2000. Defeasible logic versus logic programming without negation as failure. Journal of Logical and Algebraic Methods in Programming 42, 1, 47–57.CrossRefGoogle Scholar
Aravindan, C. and Dung, P. M. 1995. On the correctness of unfold/fold transformation of normal and extended logic programs. Journal of Logical and Algebraic Methods in Programming 24, 3, 201–217.Google Scholar
Billington, D., Antoniou, G., Governatori, G. and Maher, M. J. 2010. An inclusion theorem for defeasible logics. ACM Transactions on Computational Logic 12, 1, 6.CrossRefGoogle Scholar
Caminada, M., Sá, S., Alcântara, J. and Dvorák, W. 2015. On the equivalence between logic programming semantics and argumentation semantics. International Journal of Approximate Reasoning 58, 87–111.CrossRefGoogle Scholar
Eiter, T., Leone, N. and Saccà, D. 1997. On the partial semantics for disjunctive deductive databases. Annals of Mathematics and Artificial Intelligence 19, 1–2, 59–96.CrossRefGoogle Scholar
Fitting, M. 1985. A Kripke–Kleene semantics for logic programs. Journal of Logical and Algebraic Methods in Programming 2, 4, 295–312.CrossRefGoogle Scholar
Gelder, A. V., Ross, K. A. and Schlipf, J. S. 1991. The well-founded semantics for general logic programs. Journal of The Academy of Clinical Microbiologists 38, 3, 620–650.Google Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Proc. of JICSLP, 1070–1080.Google Scholar
Gordon, T. F. and Walton, D. 2009. Proof burdens and standards. In Argumentation in Artificial Intelligence, Rahwan, I. and Simari, G., Eds. Springer, Berlin, 239–260.Google Scholar
Governatori, G. 2011. On the relationship between Carneades and defeasible logic. In Proc. of 13th International Conference on Artificial Intelligence and Law, Ashley, K. D. and van Engers, T. M., Eds. ACM, 31–40.Google Scholar
Governatori, G., Maher, M. J., Antoniou, G. and Billington, D. 2004. Argumentation semantics for defeasible logic. Journal of Logic and Computation 14, 5, 675–702.CrossRefGoogle Scholar
Governatori, G., Olivieri, F., Scannapieco, S., Rotolo, A. and Cristani, M. 2016. The rational behind the concept of goal. Theory and Practice of Logic Programming, 16, 3, 296–324.CrossRefGoogle Scholar
Governatori, G. and Sartor, G. 2010. Burdens of proof in monological argumentation. In Proc. of 23rd Annual Conference on Legal Knowledge and Information Systems, Winkels, R., Ed. Frontiers in Artificial Intelligence and Applications, vol. 223. IOS Press, Amsterdam, 57–66.Google Scholar
Grosof, B. N. 1997. Prioritized conflict handling for logic programs. In Proc. of ILPS, 197–211.Google Scholar
Kifer, M. and Subrahmanian, V. S. 1992. Theory of generalized annotated logic programming and its applications. Journal of Logic and Computation, 12, 3&4, 335–367.Google Scholar
Kunen, K. 1987. Negation in logic programming. Journal of Logic and Computation, 4, 4, 289–308.Google Scholar
Maher, M. J. 2000. A denotational semantics of defeasible logic. In Proc. of 1st International Conference on Computational Logic – CL 2000, 24–28 July, 2000, London, UK, 209–222.Google Scholar
Maher, M. J. 2001. Propositional defeasible logic has linear complexity. Theory and Practice of Logic Programming 1, 6, 691–711.Google Scholar
Maher, M. J. 2002. A model-theoretic semantics for defeasible logic. In Proc. of ICLP 2002 Workshop Paraconsistent Computational Logic, 67–80.Google Scholar
Maher, M. J. 2012. Relative expressiveness of defeasible logics. Theory and Practice of Logic Programming, 12, 4–5, 793–810.CrossRefGoogle Scholar
Maher, M. J. 2013. Relative expressiveness of defeasible logics II. Theory and Practice of Logic Programming, 13, 4–5, 579–592.Google Scholar
Maher, M. J. 2017. Relating concrete defeasible reasoning formalisms and abstract argumentation. Fundamenta Informaticae, 153, 1, 1–28.Google Scholar
Maher, M. J. and Governatori, G. 1999. A semantic decomposition of defeasible logics. In Proc. of AAAI National Conference on Artificial Intelligence, AAAI Press, 299–305.Google Scholar
Maher, M. J., Governatori, G. and Lam, H. P. 2011. Well-founded defeasible logics, Reasoning Research Institute. Technical report.Google Scholar
Maier, F. 2013. Interdefinability of defeasible logic and logic programming under the well-founded semantics. Theory and Practice of Logic Programming, 13, 1, 107–142.CrossRefGoogle Scholar
Maier, F. and Nute, D. 2010. Well-founded semantics for defeasible logic. Synthese, 176, 2, 243–274.Google Scholar
Prakken, H. 2010. An abstract framework for argumentation with structured arguments. Argument and Computation, 1, 93–124.Google Scholar
Prakken, H. and Sartor, G. 2007. Formalising arguments about the burden of persuasion. In Proc. of 11th International Conference on Artificial Intelligence and Law, Gardner, A. and Winkels, R., Eds. ACM, 97–106.Google Scholar
Przymusinski, T. C. 1990. The well-founded semantics coincides with the three-valued stable semantics. Fundamenta Informaticae, 13, 4, 445–463.Google Scholar
Saccà, D. and Zaniolo, C. 1990. Stable models and non-determinism in logic programs with negation. In Proc. of PODS, 205–217.Google Scholar
Verheij, B. 2003. DefLog: On the logical interpretation of prima facie justified assumptions. Journal of Computer and System Sciences, 13, 3, 319–346.Google Scholar
Wan, H., Grosof, B. N., Kifer, M., Fodor, P. and Liang, S. 2009. Logic programming with defaults and argumentation theories. In Proc. of ICLP, 432–448.Google Scholar
Wan, H., Kifer, M. and Grosof, B. N. 2015. Defeasibility in answer set programs with defaults and argumentation rules. Semantic Web, 6, 1, 81–98.Google Scholar
You, J. and Yuan, L. 1994. A three-valued semantics for deductive databases and logic programs. Journal of Computer and System Sciences, 49, 2, 334–361.Google Scholar
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