Abstract
This paper establishes an explicit connection between formal argumentation and Bayesian inference by introducing a notion of argument and a notion of defeat among arguments in Bayesian networks.
First, the two approaches are compared and it is argued that argumentation in Bayesian belief networks is a typical multi-agent affair.
Since in theories of formal argumentation the so-called admissibility semantics is an important criterion of argument validity, this paper finally proposes an algorithm to decide efficiently whether a particular node is supported by an admissible argument. The proposed algorithm is then slightly extended to an algorithm that returns the top-k of strongest admissible arguments at each node. This extension is particularly interesting from a Bayesian inference point of view, because it offers a computationally tractable alternative to the NPPP-complete decision problem k-MPE (finding the top-k most probable explanations in a Bayesian network).
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References
Carofiglio, V.: Modelling argumentation with belief networks. In: Grasso, F., Reed, C., Carenini, G. (eds.) Proc. of the 4th Workshop on Computational Models of Natural Argument, CMNA 2004 (2004)
Chesñevar, C.I., Maguitman, A.G., Loui, R.P.: Logical models of argument. ACM Comput. Surv. 32(4), 337–383 (2000)
Cooper, G.F.: The computational complexity of probabilistic inference using bayesian belief networks. Artificial Intelligence 42, 393–405 (1990)
Cowell, R.G., Dawid, A.P., Lauritzen, S.L., Spiegelhalter, D.J.: Probabilistic Networks and Expert Systems. Springer, Heidelberg (1999)
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), 321–357 (1995)
Kohlas, J.: Probabilistic argumentation systems a new way to combine logic with probability. Journal of Applied Logic 1(3-4), 225–253 (2003)
Kohlas, J., Haenni, R.: Assumption-based reasoning and probabilistic argumentation systems. In: Kohlas, J., Moral, S. (eds.) Defeasible Reasoning and Uncertainty Management Systems: Algorithms, Oxford University Press, Oxford (1996)
Korb, K.B., Nicholson, A.E.: Bayesian Artificial Intelligence. Chapman and Hall/CRC Computer Science and Data Analysis (2003)
Lauritzen, S.L., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their applications to expert systems. Journal of the Royal Statistical Society, B 50, 157–224 (1988)
McConachy, R., Korb, K.B., Zuckerman, I.: A Bayesian approach to automating argumentation. In: Powers, D.M.W. (ed.) Proc. of the Joint Conf. on New Methods in Language Processing and Computational Natural Language Learning: NeMLaP3/CoNLL98, pp. 91–100. Association for Computational Linguistics, Somerset (1998)
Park, J.D.: Map complexity results and approximation methods. In: Proc. of the 18th Conf. on Uncertainty in Artificial Intelligence (UAI), pp. 388–396 (2002)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, 2nd edn. Morgan Kaufmann, Inc., Palo Alto (1994)
Pollock, J.L.: Cognitive Carpentry. A Blueprint for How to Build a Person. MIT Press, Cambridge (1995)
Pollock, J.L.: Implementing defeasible reasoning. In: Presented at the Computational Dialectics Workshop, at FAPR 1996, Bonn. Cf, June 3-7 (1996), http://nathan.gmd.de/projects/zeno/fapr/programme.html
Pollock, J.L.: Defeasible reasoning with variable degrees of justification. Artificial Intelligence Journal 133(1-2), 233–282 (2001)
Prakken, H., Vreeswijk, G.A.W.: Logics for defeasible argumentation. In: Gabby, D.H., et al. (eds.) Handbook of Philosophical Logic, pp. 219–318. Kluwer Academic Publishers, Dordrecht (2002)
Saha, S., Sen, S.: A bayes net approach to argumentation based negotiation. In: Proc. of the AAMAS-2004 workshop on Argumentation in Multi-Agent Systems, ArgMAS-2004 (2004)
Shimony, S.E.: Finding maps for belief networks is np-hard. Artificial Intelligence 68, 399–410 (1994)
Simari, G.R., Loui, R.P.: A mathematical treatment of defeasible argumentation and its implementation. Artificial Intelligence 53, 125–157 (1992)
Toulmin, S.: The Uses of Argument. Cambridge University Press, Cambridge (1985)
Bart Verheij, H.: Accrual of arguments in defeasible argumentation. In: Witteveen, C., van der Hoek, W., Meyer, J.-J.Ch., van Linder, B. (eds.) Proc. of the 2nd Dutch/German Workshop on Nonmonotonic Reasoning, Utrecht, pp. 217–224 (1995)
Vreeswijk, G., Prakken, H.: Credulous and sceptical argument games for preferred semantics. In: Brewka, G., Moniz Pereira, L., Ojeda-Aciego, M., de Guzmán, I.P. (eds.) JELIA 2000. LNCS (LNAI), vol. 1919, pp. 239–253. Springer, Heidelberg (2000)
Vreeswijk, G.A.W.: IACAS: An implementation of Chisholm’s principles of knowledge. In: Witteveen, C., van der Hoek, W., Meyer, J.-J.C., van Linder, B. (eds.) The Proc. of the 2nd Dutch/German Workshop on Nonmonotonic Reasoning, Utrecht, pp. 225–234. Delft University of Technology, University of Utrecht (1995)
Zhang, N.L., Poole, D.: Exploiting causal independence in bayesian network inference. Journal of Artificial Intelligence Research 5, 301–328 (1996)
Zukerman, I., McConachy, R., Korb, K.B., Pickett, D.: Exploratory interaction with a bayesian argumentation system. In: Dean, T. (ed.) Proc. of the 16th Int. Joint Conf. on Artificial Intelligence (IJCAI 1999), pp. 1294–1299. Morgan Kaufmann, San Francisco (1999)
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Vreeswijk, G.A.W. (2005). Argumentation in Bayesian Belief Networks. In: Rahwan, I., Moraïtis, P., Reed, C. (eds) Argumentation in Multi-Agent Systems. ArgMAS 2004. Lecture Notes in Computer Science(), vol 3366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32261-0_8
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