Abstract
In a recent paper [2] the authors have formalized a recursive semantics for warranted conclusions in a general defeasible argumentation framework based on a propositional logic. The warrant recursive semantics is based on a general notion of collective (non-binary) conflict among arguments allowing to ensure direct and indirect consistency properties. This general framework has also been extended with levels of defeasibility and with a level-wise recursive definition of warranted and blocked conclusions. In this paper we focus on the recursive semantics for the particular framework of Defeasible Logic Programming (DeLP) extended with levels of defeasibility, called RP-DeLP, for which we characterize programs with a unique output (extension) for warranted conclusions, and we design, for this type of programs, an algorithm for computing warranted conclusions in polynomial space and with an upper bound on complexity equal to P NP.
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References
Alsinet, T., Chesñevar, C.I., Godo, L., Simari, G.: A logic programming framework for possibilistic argumentation: Formalization and logical properties. Fuzzy Sets and Systems 159(10), 1208–1228 (2008)
Alsinet, T., Béjar, R., Godo, L.: A characterization of collective conflict for defeasible argumentation. In: Proc. of COMMA 2010, pp. 27–38 (2010)
Alsinet, T., Chesñevar, C.I., Godo, L.: A Level-based Approach to Computing Warranted Arguments in Possibilistic Defeasible Logic. In: Proc. of COMMA 2008, pp. 1–12 (2008)
Besnard, P., Hunter, A.: Elements of Argumentation. The MIT Press, Cambridge (2008)
Bondarenko, A., Dung, P.M., Kowalski, R.A., Toni, F.: An abstract, argumentation-theoretic approach to default reasoning. Artif. Intell. 93, 63–101 (1997)
Caminada, M., Amgoud, L.: On the evaluation of argumentation formalisms. Artif. Intell. 171(5-6), 286–310 (2007)
Cecchi, L., Fillottrani, P., Simari, G.: On the complexity of DeLP through game semantics. In: Proc. of NMR 2006, pp. 386–394 (2006)
Chesñevar, C.I., Maguitman, A., Loui, R.: Logical Models of Argument. ACM Computing Surveys 32(4), 337–383 (2000)
Chesñevar, C.I., Simari, G., Godo, L.: Computing dialectical trees efficiently in possibilistic defeasible logic programming. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS (LNAI), vol. 3662, pp. 158–171. Springer, Heidelberg (2005)
Dimopoulos, Y., Torres, A.: Graph theoretical structures in logic programs and default theories. Theoretical Computer Science 170(1-2), 209–244 (1996)
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)
Dung, P.M., Mancarella, P., Toni, F.: A dialectic procedure for sceptical, assumption-based argumentation. In: Proc. of COMMA 2006, pp. 145–156 (2006)
Dung, P.M., Mancarella, P., Toni, F.: Computing ideal sceptical argumentation. Artif. Intell. 171(10-15), 642–674 (2007)
Dunne, P.E.: The computational complexity of ideal semantics. Artif. Intell. 173(18), 1559–1591 (2009)
Dunne, P.E., Bench-Capon, T.J.M.: Coherence in finite argument systems. Artif. Intell. 141(1-2), 187–203 (2002)
Dunne, P.E.: The computational complexity of ideal semantics i: Abstract argumentation frameworks. In: Proc. of COMMA 2008, pp. 147–158 (2008)
García, A., Simari, G.: Defeasible Logic Programming: An Argumentative Approach. Theory and Practice of Logic Programming 4(1), 95–138 (2004)
Hirsch, R., Gorogiannis, N.: The complexity of the warranted formula problem in propositional argumentation. J. of Logic and Computation 20(2) (2009)
Pollock, J.L.: A recursive semantics for defeasible reasoning. In: Rahwan, I., Simari, G. (eds.) Argumentation in Artificial Intelligence. ch. 9, pp. 173–198. Springer, Heidelberg (2009)
Prakken, H., Sartor, G.: Argument-based extended logic programming with defeasible priorities. J. of Applied Non-classical Logics 7, 25–75 (1997)
Prakken, H., Vreeswijk, G.: Logical Systems for Defeasible Argumentation. In: Gabbay, D., Guenther, F. (eds.) Handbook of Phil. Logic, pp. 219–318. Kluwer, Dordrecht (2002)
Rahwan, I., Simari, G. (eds.): Argumentation in Artificial Intelligence. Springer, Heidelberg (2009)
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Alsinet, T., Béjar, R., Godo, L. (2010). A Computational Method for Defeasible Argumentation Based on a Recursive Warrant Semantics. In: Kuri-Morales, A., Simari, G.R. (eds) Advances in Artificial Intelligence – IBERAMIA 2010. IBERAMIA 2010. Lecture Notes in Computer Science(), vol 6433. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16952-6_5
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