Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-19T02:14:54.920Z Has data issue: false hasContentIssue false
  • English
  • Français

Preferred extensions as stable models*

Published online by Cambridge University Press:  08 May 2008

JUAN CARLOS NIEVES ,
ULISES CORTÉS  and
MAURICIO OSORIO
JUAN CARLOS NIEVES
Affiliation:
Universitat Politècnica de Catalunya, Software Department (LSI), c/Jordi Girona 1-3, E08034, Barcelona, Spain (e-mail: [email protected], [email protected])
ULISES CORTÉS
Affiliation:
Universitat Politècnica de Catalunya, Software Department (LSI), c/Jordi Girona 1-3, E08034, Barcelona, Spain (e-mail: [email protected], [email protected])
MAURICIO OSORIO
Affiliation:
Universidad de las Américas – Puebla, CENTIA, Sta. Catarina Mártir, Cholula, Puebla, 72820México (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

Given an argumentation framework AF, we introduce a mapping function that constructs a disjunctive logic program P, such that the preferred extensions of AF correspond to the stable models of P, after intersecting each stable model with the relevant atoms. The given mapping function is of polynomial size w.r.t. AF.

In particular, we identify that there is a direct relationship between the minimal models of a propositional formula and the preferred extensions of an argumentation framework by working on representing the defeated arguments. Then we show how to infer the preferred extensions of an argumentation framework by using UNSAT algorithms and disjunctive stable model solvers. The relevance of this result is that we define a direct relationship between one of the most satisfactory argumentation semantics and one of the most successful approach of nonmonotonic reasoning i.e., logic programming with the stable model semantics.

Keywords

preferred semanticsabstract argumentation semanticsstable model semanticsminimal models
Type
Technical Note
Information
Theory and Practice of Logic Programming , Volume 8 , Issue 4 , July 2008 , pp. 527 - 543
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

ASPIC: Project. 2005. Deliverable D2.2:Formal semantics for inference and decision-making. Argumentation Service Plarform with Integrated Components.Google Scholar
ASPIC: Project. 2006. ASPIC: Argumentation engine demo. URL: !http://aspic.acl.icnet.uk/.Google Scholar
Ben-Eliyahu-Zohary, R. 2005. An incremental algorithm for generating all minimal models. Artificial Intelligence 169, 1, 1–22.Google Scholar
Bench-Capon, T. 2002. Value-based argumentation frameworks. In Proceedings of Non Monotonic Reasoning, 444–453.Google Scholar
Besnard, P. and Doutre, S. 2004. Checking the acceptability of a set of arguments. In Tenth International Workshop on Non-Monotonic Reasoning (NMR 2004), 59–64.Google Scholar
Bondarenko, A., Dung, P. M., Kowalski, R. A. and Toni, F. 1997. An abstract, argumentation-theoretic approach to default reasoning. Artificial Intelligence 93, 63–101.Google Scholar
Cayrol, C., Doutre, S. and Mengin, J. 2003. On decision problems related to the preferred semantics for argumentation frameworks. Journal of Logic and Computation 13, 3, 377–403.Google Scholar
Cortés, U., Tolchinsky, P., Nieves, J. C., López-Navidad, A. and Caballero, F. 2005. Arguing the discard of organs for transplantation in CARREL. In CATAI 2005, 93–105.Google Scholar
Dimopoulos, Y. and Torres, A. 1996. Graph theoretical structures in logic programs and default theories. Theoretical Computer Science 170, 1–2, 209–244.Google Scholar
DLV, S. 1996. Vienna University of Technology. URL: http://www.dbai.tuwien.ac.at/proj/dlv/.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, 321–358.CrossRefGoogle Scholar
Dung, P. M., Kowalski, R. A. and Toni, F. 2006. Dialectic proof procedures for assumption-based, admissible argumentation. Artificial Intelligence 170, 2, 114–159.CrossRefGoogle Scholar
Dung, P. M., Mancarella, P. and Toni, F. 2007. Computing ideal sceptical argumentation. Artificial Intelligence 171, 10–15, 642–674.Google Scholar
Dunne, P. E. and Bench-Capon, T. J. M. 2004. Complexity in value-based argument systems. In JELIA. Lecture Notes in Computer Science, vol. 3229. Springer, Berlin, 360–371.Google Scholar
Egly, U. and Woltran, S. 2006. Reasoning in argumentation frameworks using quantified Boolean formulas. In Proceedings of COMMA, Dunne, P. E. and Bench-Capon, T. J., Eds. Frontiers in Artificial Intelligence and Applications, vol. 144. IOS Press, Amsterdam, 133–144.Google Scholar
Gaertner, D. and Toni, F. 2007. CaSAPI: A system for credulous and sceptical argumentation. In Argumentation and Non-Monotonic Reasoning (LPNMR-07 Workshop), Simari, G. and Torroni, P., Eds. Arizona, USA, 80–95.Google Scholar
Gebser, M., Liu, L., Namasivayam, G., Neumann, A., Schaub, T. and Truszczynski, M. 2007. The first answer set programming system competition. In Ninth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR-07), Baral, G. B. Chitta and Schlipf, J., Eds. Lecture Notes in Artificial Intelligence, vol. 4483. Springer-Verlag, Berlin, 3–17.CrossRefGoogle Scholar
Gelder, A. V., Ross, K. A. and Schlipf, J. S. 1991. The well-founded semantics for general logic programs. Journal of the ACM 38, 3, 620–650.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385.Google Scholar
Leone, N., Pfeifer, G., Faber, W., Calimeri, F., Dell'Armi, T., Eiter, T., Gottlob, G., Ianni, G., Ielpa, G., Koch, C., Perri, S. and Polleres, A. 2002. The dlv system. In JELIA, 537–540.Google Scholar
Nieves, J. C., Osorio, M., Cortés, U., Olmos, I. and Gonzalez, J. A. 2006. Defining new argumentation-based semantics by minimal models. In Seventh Mexican International Conference on Computer Science (ENC 2006). IEEE Computer Science Press, Los Alamitos, California, 210–220.CrossRefGoogle Scholar
Nieves, J. C., Osorio, M., and Cortés, U. 2008. Studying the Grounded Semantics by Using a Suitable Codification. Research report LSI-08-6-R, Universitat Politècnica de Catalunya, Software Department (LSI), Barcelona, Spain.Google Scholar
Osorio, M., Navarro, J. A. and Arrazola, J. 2004. Applications of intuitionistic logic in answer set programming. Theory and Practice of Logic Programming (TPLP) 4, 3, 225–354.Google Scholar
Pollock, J. L. 1995. Cognitive Carpentry: A Blueprint for How to Build a Person. MIT Press, Cambridge, MA.CrossRefGoogle 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, 219–318.Google Scholar
Ricca, F. 2003. The dlv java wrapper. In 2003 Joint Conference on Declarative Programming, AGP-2003, Reggio Calabria, Italy, 3–5 September 2003, 263–274.Google Scholar
Tolchinsky, P., Cortés, U., Nieves, J. C., López-Navidad, A. and Caballero, F. 2005. Using arguing agents to increase the human organ pool for transplantation. In Proceedings of the Third Workshop on Agents Applied in Health Care (IJCAI 2005).Google Scholar
vanDalen, D. Dalen, D. 1994. Logic and Structure, 3rd augmented ed. Springer-Verlag, Berlin.Google Scholar