A Schema for Generating Relevant Logic Programming Semantics and its Applications in Argumentation Theory

• Autorzy: Nieves, J.C. , Osorio, M. , Zepeda, C.
• Języki publikacji: EN

Abstrakty

EN

In the literature, there are several approaches which try to perform common sense reasoning. Among them, the approaches which have probably received the most attention the last two decades are the approaches based on logic programming semantics with negation as failure and argumentation theory. Even though both approaches have their own features, it seems that they share some common behaviours which can be studied by considering the close relationship between logic programming semantics and extension-based argumentation semantics. In this paper, we will present a general recursive schema for defining new logic programming semantics. This schema takes as input any basic logic programming semantics, such as the stable model semantics, and gives as output a new logic programming semantics which satisfies some desired properties such as relevance and the existence of the intended models for every normal program. We will see that these new logic programming semantics can define candidate extension-based argumentation semantics. These new argumentation semantics will overcome some of the weakness of the extension-based argumentation semantics based on admissible sets. In fact, we will see that some of these new argumentation semantics have similar behaviour to the extension-based argumentation semantics built in terms of strongly connected components.

Słowa kluczowe

EN

non-monotonic reasoning; extension-based argumentation semantics; logic programming semantics; Logic Programming (LP)

• Czasopismo: Fundamenta Informaticae
• Rocznik: 2011
• Tom: Vol. 106, nr 2-4
• Strony: 295-311
• Opis fizyczny: Bibliogr. 48 poz.

Twórcy

autor

Nieves, J.C.

autor

Osorio, M.

autor

Zepeda, C.

• Universitat Politčcnica de Catalunya. Software Department (LSI). c/Jordi Girona 1-3, E08034, Barcelona, Spain.,

Bibliografia

• [1] Balduccini, M., Gelfond, M.: Logic Programs with Consistency-Restoring Rules, International Symposium on Logical Formalization of Commonsense Reasoning (P. Doherty, J. McCarthy, M.-A. Williams, Eds.), AAAI 2003 Spring Symposium Series, Mar 2003.
• [2] Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving, Cambridge University Press, Cambridge, 2003.
• [3] Baroni, P., Giacomin, M.: On principle-based evaluation of extension-based argumentation semantics, Artificial Intelligence., 171(10-15), 2007, 675-700.
• [4] Baroni, P., Giacomin, M., Guida, G.: SCC-recursiveness: a general schema for argumentation semantics, Artificial Intelligence, 168, October 2005, 162-210.
• [5] Bench-Capon, T. J. M., Dunne, P. E.: Argumentation in artificial intelligence, Artificial Intelligence, 171(10-15), 2007, 619-641.
• [6] Brass, S., Zukowski, U., Freitag, B.: Transformation-Based Bottom-Up Computation of the Well-Founded Model., NMELP, 1996.
• [7] Brewka, G.: An Abductive Framework for Generalized Logic Programs, LPNMR, 1993.
• [8] Caminada, M.: Contamination in Formal Argumentation Systems., BNAIC 2005 - Proceedings of the Seventeenth Belgium-Netherlands Conference on Artificial Intelligence, Brussels, Belgium, October 17-18, 2005.
• [9] Caminada, M.: Semi-Stable Semantics, Proceedings of COMMA (P. E. Dunne, T. J. Bench-Capon, Eds.), 144, IOS Press, 2006.
• [10] Caminada, M., Sakama, C.: On the Existence of Answer Sets in Normal Extended Logic Programs., ECAI, 2006.
• [11] Carballido, J. L., Nieves, J. C., Osorio, M.: Inferring Preferred Extensions by Pstable Semantics, Revista Iberomericana de Inteligencia Artificial, 13(41), 2009, 38-53.
• [12] Cormen, T. H., Leiserson, C. E., Riverst, R. L., Stein, C.: Introduction to Algorithms, Second edition, MIT Press, 2001.
• [13] van Dalen, D.: Logic and structure, 3rd., aumented edition edition, Springer-Verlag, Berlin, 1994.
• [14] Denecker,M., Pelov, N., Bruynooghe,M.: Ultimate Well-founded and Stable Semantics for Logic Programs with Aggregates, In Proceedings of ICLP-01, LNCS 2237, Springer, 2001.
• [15] Dix, J.: A Framework for Representing and Characterizing Semantics of Logic Programs, KR, 1992.
• [16] Dix, J.: A Classification Theory of Semantics of Normal Logic Programs: I. Strong Properties., Fundam. Inform., 22(3), 1995, 227-255.
• [17] Dix, J.: A Classification Theory of Semantics of Normal Logic Programs: II. Weak Properties., Fundam. Inform., 22(3), 1995, 257-288.
• [18] Dix, J., Müller, M.: Partial Evaluation and Relevance for Approximations of Stable Semantics, ISMIS, 869, Springer, 1994.
• [19] Dix, J., Müller, M.: The Stable Semantics and its Variants: A Comparison of Recent Approaches, KI, 1994.
• [20] Dix, J., Osorio, M., Zepeda, C.: A general theory of confluent rewriting systems for logic programming and its applications., Ann. Pure Appl. Logic, 108(1-3), 2001, 153-188.
• [21] Dung, P. M.: On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and n-Person Games., Artificial Intelligence, 77(2), 1995, 321-358.
• [22] Dung, P. M., Mancarella, P., Toni, F.: Computing ideal sceptical argumentation, Artif. Intell., 171(10-15), 2007, 642-674.
• [23] Egly, U., Gaggl, S. A., Woltran, S.: ASPARTIX: Implementing Argumentation Frameworks Using Answer-Set Programmin, International Conference of Logic Programming (ICLP) (M. G. de la Banda, E. Pontelli, Eds.), 5366, Springer, 2008.
• [24] Ferraris, P., Lee, J., Lifschitz, V., Palla, R.: Symmetric Splitting in the General Theory of Stable Models, IJCAI, 2009.
• [25] Gelder, A. V., Ross, K. A., Schlipf, J. S.: TheWell-Founded Semantics for General Logic Programs., Journal of the ACM, 38(3), 1991, 620-650.
• [26] Gelfond, M., Lifschitz, V.: The Stable Model Semantics for Logic Programming, 5th Conference on Logic Programming (R. Kowalski, K. Bowen, Eds.), MIT Press, 1988.
• [27] Jakobovits, H., Vermeir, D.: Robust semantics for argumentation frameworks, Journal of logic and computation, 9(2), 1999, 215-261.
• [28] Kakas, A. C., Kowalski, R. A., Toni, F.: The role of Abduction in Logic Programming, in: Handbook in Artificial Intelligence and Logic Programming, Volume 5 (D. Gabbay, C. J. Hogger, J. A. Robinson, Eds.), Oxford University Press, Oxford, 1998, 235-324.
• [29] Kakas, A. C., Mancarella, P.: Generalized Stable Models: A Semantics for Abduction, ECAI, 1990.
• [30] L. M. Pereira, A. M. P.: Layer Supported Models of Logic Programs (extended version). Submitted to LANMR'09. Online: http://centria.fct.unl.pt/ lmp/ (Last consulted 13/08/09).
• [31] Lifschitz, V., Turner, H.: Splitting a Logic Program, ICLP, 1994.
• [32] Lloyd, J. W.: Foundations of Logic Programming, Springer, Berlin, 1987.
• [33] Nieves, J. C.: Modeling arguments and uncertain information - A non-monotonic reasoning approach, Ph.D. Thesis, Software Department (LSI), Technical University of Catalonia, 2008.
• [34] Nieves, J. C., Osorio, M., Cortés, U.: Inferring Preferred Extensions by Minimal Models, Argumentation and Non-Monotonic Reasoning (LPNMR-07 Workshop) (G. Simari, P. Torroni, Eds.), Arizona, USA, 2007.
• [35] Nieves, J. C., Osorio, M., Cortés, U.: Preferred Extensions as Stable Models, Theory and Practice of Logic Programming, 8(4), July 2008, 527-543.
• [36] Nieves, J. C., Osorio, M., Cortés, U.: Studying the grounded semantics by using a suitable codification, Research report LSI-08-6-R, Universitat Politècnica de Catalunya, Software Department (LSI), Barcelona, Spain, January 2008.
• [37] Nieves, J. C., Osorio, M., Cortés, U., Olmos, I., Gonzalez, J. A.: Defining new argumentation-based semantics by minimal models, Seventh Mexican International Conference on Computer Science (ENC 2006), IEEE Computer Science Press, September 2006.
• [38] Nieves, J. C., Osorio, M., Zepeda, C.: Expressing Extension-Based Semantics Based on Stratified Minimal Models, WoLLIC 2009, Tokyo, Japan, June 21-24, 2009. Proceedings, 5514, Springer, 2009.
• [39] Osorio, M., Navarro, J. A., Arrazola, J. R., Borja, V.: Logics with Common Weak Completions, Journal of Logic and Computation, 16(6), 2006, 867-890.
• [40] Osorio, M., Nieves, J. C.: Ws,c-Stable Semantics for Propositional Theories, International Conferences of CIC'2001, México, 2001.
• [41] Pereira, L.M., Pinto, A.M.: Revised StableModels - A Semantics for Logic Programs, EPIA, 3808, Springer, 2005.
• [42] Pereira, L. M., Pinto, A. M.: Approved Models for Normal Logic Programs, LPAR 2007, 4790, Springer, 2007.
• [43] Pereira, L. M., Pinto, A. M.: Layer Supported Models of Logic Programs, LPNMR 2009, 5753, Springer, 2009.
• [44] Pollock, J. L.: Justification and Defeat, Artif. Intell., 67(2), 1994, 377-407.
• [45] Prakken, H., Vreeswijk, G. A. W.: Logics for defeasible argumentation, in: Handbook of Philosophical Logic (D. Gabbay, F. Günthner, Eds.), vol. 4, second edition, Kluwer Academic Publishers, Dordrecht/Boston/London, 2002, 219-318.
• [46] Schlipf, J. S.: Formalizing a Logic for Logic Programming, Ann. Math. Artif. Intell., 5(2-4), 1992, 279-302.
• [47] Wakaki, T., Nitta, K.: Computing Argumentatoin Semantics in Answer Set Progamming, JSAI'2008, 5447, 2009.
• [48] Wu, Y., Caminada, M., Gabbay, D. M.: Complete Extensions in Argumentation Coincide with 3-Valued Stable Models in Logic Programming, Studia Logica, 93(2-3), 2009, 383-403.