Abstract
This paper studies methodologically robust options for giving logical contents to nodes in abstract argumentation networks. It defines a variety of notions of attack in terms of the logical contents of the nodes in a network. General properties of logics are refined both in the object level and in the metalevel to suit the needs of the application. The network-based system improves upon some of the attempts in the literature to define attacks in terms of defeasible proofs, the so-called rule-based systems. We also provide a number of examples and consider a rigorous case study, which indicate that our system does not suffer from anomalies. We define consequence relations based on a notion of defeat, consider rationality postulates, and prove that one such consequence relation is consistent.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Alchourron C.E., Gardenfors P., Makinson D.C.: ‘On the Logic of Theory Change: Partial Meet Contraction and Revision Functions’. The Journal of Symbolic Logic 50, 510–530 (1985)
Barringer, H., D. M. Gabbay, and J. Woods, ‘Temporal Dynamics of Support and Attack Networks: From Argumentation to Zoology’, in D. Hutter and W. Stephan (eds.), Mechanising Mathematical Reasoning, LNCS 2605: 59–98, Springer, 2005.
Besnard, P., and A. B. Hunter, Elements of Argumentation, MIT Press, 2008.
Caminada M.W.A., Amgoud L.: ‘On the evaluation of argumentation formalisms’. Artificial Intelligence 171(5–6), 286–310 (2007)
d’Avila Garcez, A. S., K. Broda, and D. M. Gabbay, Neural-Symbolic Learning Systems: Foundations and Applications, Springer, 2002.
d’Avila Garcez, D. M. Gabbay, and L. C. Lamb, ‘Value-based Argumentation Frameworks as Neural-Symbolic Learning Systems’, Journal of Logic and Computation 15(6): 1041-1058 December 2005.
d’Avila Garcez, and D. M. Gabbay, ‘Fibring Neural Networks’, in Proc. 19th National Conference on Artificial Intelligence AAAI 2004, San Jose, California, USA, AAAI Press, July 2004.
d’Avila Garcez, L. C. Lamb, and D.M. Gabbay, Neural-Symbolic Cognitive Reasoning, Springer, 2008.
Gabbay, D. M., Labelled Deductive Systems, OUP, 1996.
Gabbay D.M., Reyle U.: ‘N-Prolog: An Extension of Prolog with Hypothetical Implications’. Journal of Logic Programming 1(4), 319–355 (1984)
Gabbay, D. M., Fibring Logics, OUP, 1998.
Gabbay D.M., Woods J.: ‘Resource origins of non-monotonicity’. Studia Logica 88(1), 85–112 (2008)
Gomez Lucero, M. J., C. I. Chesnevar and G. R. Simari, ‘On the Accrual of Arguments in Defeasible Logic Programming’, in Proc. 21st Intl. Joint Conference on Artificial Intelligence IJCAI 2009, Pasadena, USA, July 2009 (in press).
Leitgeb, H., ‘Neural network models of conditionals: an introduction’, in X. Arrazola, J. M. Larrazabal et al. (eds.), Proc. ILCLI International Workshop on Logic and Philosophy of Knowledge, Communication and Action, 191-223, Bilbao, 2007.
Pollock J.: ‘Self-defeating Arguments’. Minds and Machines 1(4), 367–392 (1991)
Verheij, B., ‘Accrual of arguments in defeasible argumentation’, in Proc. 2nd Dutch/German Workshop on Nonmonotonic Reasoning, Utrecht, 217–224, 1995.
Prakken H., Sartor G.: ‘Argument based extended logic programming with defeasible priorities’. Joural of Applied Non-classical Logics 7, 25–75 (1997)
Stenning, K., and M. van Lambalgen, Human reasoning and cognitive science, MIT Press, 2008.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gabbay, D.M., Garcez, A.S.d. Logical Modes of Attack in Argumentation Networks. Stud Logica 93, 199 (2009). https://doi.org/10.1007/s11225-009-9216-z
Published:
DOI: https://doi.org/10.1007/s11225-009-9216-z