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Range-based argumentation semantics as two-valued models

Published online by Cambridge University Press:  03 May 2016

MAURICIO OSORIO
Affiliation:
Universidad de las Américas - Puebla, Depto. de Actuaría, Física y Matemáticas, Sta. Catarina Mártir, Cholula, Puebla, 72820México (e-mail: osoriomauri@gmail.com)
JUAN CARLOS NIEVES
Affiliation:
Department of Computing Science, Umeå University SE-901 87, Umeå, Sweden (e-mail: jcnieves@cs.umu.se)

Abstract

Characterizations of semi-stable and stage extensions in terms of two-valued logical models are presented. To this end, the so-called GL-supported and GL-stage models are defined. These two classes of logical models are logic programming counterparts of the notion of range which is an established concept in argumentation semantics.

Type
Technical Note
Copyright
Copyright © Cambridge University Press 2016 

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References

Baral, C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge.Google Scholar
Baroni, P., Caminada, M. and Giacomin, M. 2011. An introduction to argumentation semantics. Knowledge Eng. Review 26, 4, 365410.Google Scholar
Caminada, M. 2006. Semi-stable semantics. In Proc. of COMMA, Dunne, P. E. and Bench-Capon, T. J., Eds. vol. 144. IOS Press, Netherlands, 121130.Google Scholar
Caminada, M., , S. and Alcântara, J. 2013. On the Equivalence between Logic Programming Semantics and Argumentation Semantics. Technical Report ABDN-CS-13-01, University of Aberdeen.CrossRefGoogle Scholar
Caminada, M. W. A., Carnielli, W. A. and Dunne, P. E. 2012. Semi-stable semantics. Journal of Logic and Computation 22, 5, 12071254.Google Scholar
Carballido, J. L., Nieves, J. C. and Osorio, M. 2009. Inferring preferred extensions by pstable semantics. Iberoamerican Journal of Artificial Intelligence (Inteligencia Artificial) ISSN: 1137-3601, (doi: 10.4114/ia.v13i41.1029) 13, 41, 3853.Google Scholar
Charwat, G., Dvorák, W., Gaggl, S. A., Wallner, J. P. and Woltran, S. 2015. Methods for solving reasoning problems in abstract argumentation - A survey. Artificial Intelligence 220, 2863.Google Scholar
Dung, P. M. 1995. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence 77, 2, 321358.Google Scholar
Dvorák, W. and Woltran, S. 2010. Complexity of semi-stable and stage semantics in argumentation frameworks. Information Processing Letters 110, 11, 425430.CrossRefGoogle Scholar
Egly, U., Alice Gaggl, S. and Woltran, S. 2010. Answer-set programming encodings for argumentation frameworks. Argument and Computation 1, 2, 147177.Google Scholar
Gabbay, D. M. and d'Avila Garcez, A. S. 2009. Logical modes of attack in argumentation networks. Studia Logica 93, 2–3, 199230.CrossRefGoogle Scholar
Gelfond, M. 2008. Handbook of Knowledge Representation. Elsevier, Chapter Answer Sets, Maryland Heights, MO, 285316.CrossRefGoogle Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Proc. 5th Conference on Logic Programming, Kowalski, R. and Bowen, K., Eds. MIT Press, Cambridge, MA, 10701080.Google Scholar
Nieves, J. C. and Osorio, M. 2014. Ideal extensions as logical programming models. Journal of Logic and Computation DOI:10.1093/logcom/exu014.Google Scholar
Nieves, J. C., Osorio, M. and Cortés, U. 2008. Preferred extensions as stable models. Theory and Practice of Logic Programming 8, 4 (July), 527543.Google Scholar
Nieves, J. C., Osorio, M. and Zepeda, C. 2011. A schema for generating relevant logic programming semantics and its applications in argumentation theory. Fundamenta Informaticae 106, 2–4, 295319.Google Scholar
Nieves, J. C., Osorio, M., Zepeda, C. and Cortés, U. 2005. Inferring acceptable arguments with answer set programming. In Proc. 6th Mexican International Conference on Computer Science (ENC 2005). IEEE Computer Science Press, 198205.Google Scholar
Osorio, M., Navarro, J. A., Arrazola, J. R. and Borja, V. 2006. Logics with common weak completions. Journal of Logic and Computation 16, 6, 867890.Google Scholar
Osorio, M., Nieves, J. C. and Santoyo, A. 2013. Complete extensions as Clark's completion semantics. In Mexican International Conference on Computer Science. IEEE Computer Science Press, 8188.Google Scholar
Prakken, H. and Vreeswijk, G. A. W. 2002. Logics for defeasible argumentation. In Handbook of Philosophical Logic, 2nd ed., Vol. 4, Gabbay, D. and Günthner, F., Eds. Kluwer Academic Publishers, Dordrecht/Boston/London, 219318.Google Scholar
Strass, H. 2013. Approximating operators and semantics for abstract dialectical frameworks. Artif. Intell. 205, 3970.Google Scholar
Toni, F. and Sergot, M. 2011. Argumentation and answer set programming. In Logic Programming, Knowledge Representation, and Nonmonotonic Reasoning, Balduccini, M. and Son, T. C., Eds., vol. 6565. LNCS, Springer, 164180.CrossRefGoogle Scholar
Verheij, B. 1996. Two approaches to dialectical argumentation: admissible sets and argumentation stages. In Proc. of the 8th Dutch Conference on Artificial Intelligence (NAIC 1996), 357–368.Google Scholar
Wu, Y., Caminada, M. and Gabbay, D. M. 2009. Complete extensions in argumentation coincide with 3-valued stable models in logic programming. Studia Logica 93, 2–3, 383403.Google Scholar