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A labelling framework for probabilistic argumentation. (English) Zbl 06909218
Summary: The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic argumentation is approached in the literature with different frameworks, pertaining to structured and abstract argumentation, and with respect to diverse types of uncertainty, in particular the uncertainty on the credibility of the premises, the uncertainty about which arguments to consider, and the uncertainty on the acceptance status of arguments or statements. Towards a general framework for probabilistic argumentation, we investigate a labelling-oriented framework encompassing a basic setting for rule-based argumentation and its (semi-) abstract account, along with diverse types of uncertainty. Our framework provides a systematic treatment of various kinds of uncertainty and of their relationships and allows us to back or question assertions from the literature.

MSC:
03H99 Nonstandard models
Software:
AFRA; PRISM
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[1] Atkinson, K; Baroni, P; Giacomin, M; Hunter, A; Prakken, H; Reed, C; Simari, GR; Thimm, M; Villata, S, Towards artificial argumentation, AI Mag., 38, 25-36, (2017)
[2] Baroni, P; Caminada, M; Giacomin, M, An introduction to argumentation semantics, Knowl. Eng. Rev., 26, 365-410, (2011)
[3] Baroni, P; Cerutti, F; Giacomin, M; Guida, G, AFRA: argumentation framework with recursive attacks, Int. J. Approx. Reason., 52, 19-37, (2011) · Zbl 1211.68433
[4] Baroni, P., Giacomin, M., Vicig, P.: On rationality conditions for epistemic probabilities in abstract argumentation. In: Proc. of the 5th Inf. Conf. on Computational Models of Argument (COMMA 2014), Frontiers in Artificial Intelligence and Applications, vol. 266, pp. 121-132. IOS Press (2014)
[5] Baroni, P., Governatori, G., Riveret, R.: On labelling statements in multi-labelling argumentation. In: Proc. of the 22nd European Conf. on Artificial Intelligence (ECAI 2016), Frontiers in Artificial Intelligence and Applications, vol. 285, pp. 489-497. IOS Press (2016) · Zbl 1403.68252
[6] Bench-Capon, T; Dunne, PE, Argumentation in artificial intelligence, Artif. Intell., 171, 619-641, (2007) · Zbl 1168.68560
[7] Bondarenko, A; Dung, PM; Kowalski, RA; Toni, F, An abstract, argumentation-theoretic approach to default reasoning, Artif. Intell., 93, 63-101, (1997) · Zbl 1017.03511
[8] Cayrol, C; Lagasquie-Schiex, M, Bipolarity in argumentation graphs: towards a better understanding, Int. J. Approx. Reason., 54, 876-899, (2013) · Zbl 1316.68152
[9] Cohen, A; Gottifredi, S; García, AJ; Simari, GR, An approach to abstract argumentation with recursive attack and support, J. Appl. Log., 13, 509-533, (2015) · Zbl 1386.68156
[10] De Finetti, B.: Theory of probability: a critical introductory treatment. Wiley, New York (1974) · Zbl 0328.60002
[11] Dondio, P, Toward a computational analysis of probabilistic argumentation frameworks, Cybern. Syst., 45, 254-278, (2014) · Zbl 1331.68221
[12] Dung, PM, On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games, Artif. Intell., 77, 321-358, (1995) · Zbl 1013.68556
[13] Dung, P.M., Thang, P.M.: Towards (probabilistic) argumentation for jury-based dispute resolution. In: Proc. of the 3rd Int. Conf. on Computational Models of Argument (COMMA 2010), Frontiers in Artificial Intelligence and Applications, vol. 216, pp. 171-182. IOS Press (2010)
[14] Dung, PM; Thang, PM, Closure and consistency in logic-associated argumentation, J. Artif. Intell. Res., 49, 79-109, (2014) · Zbl 1361.68225
[15] Fazzinga, B., Flesca, S., Parisi, F.: On the complexity of probabilistic abstract argumentation. In: Proc. of the 23rd Int. Joint Conf. on Artificial Intelligence, IJCAI 2013, pp. 898-904. AAAI Press (2013) · Zbl 1354.68253
[16] Fazzinga, B; Flesca, S; Parisi, F, On the complexity of probabilistic abstract argumentation frameworks, ACM Trans. Comput. Log, 16, 22, (2015) · Zbl 1354.68253
[17] Fazzinga, B; Flesca, S; Parisi, F, On efficiently estimating the probability of extensions in abstract argumentation frameworks, Int. J. Approx. Reason., 69, 106-132, (2016) · Zbl 1344.68221
[18] Fenton, NE; Neil, M; Lagnado, DA, A general structure for legal arguments about evidence using Bayesian networks, Cogn. Sci., 37, 61-102, (2013)
[19] Fruhwirth, T.: Constraint Handling Rules, 1st edn. Cambridge University Press, Cambridge (2009) · Zbl 1182.68039
[20] Gabbay, DM; Rodrigues, O, Probabilistic argumentation: an equational approach, Log. Univers., 9, 345-382, (2015) · Zbl 1337.68241
[21] Garcia, AJ; Simari, GR, Defeasible logic programming: delp servers, contextual queries, and explanations for answers, Argument & Computation, 5, 63-88, (2014)
[22] Governatori, G; Maher, MJ; Antoniou, G; Billington, D, Argumentation semantics for defeasible logic, J. Log. Comput., 14, 675-702, (2004) · Zbl 1067.03038
[23] Grabmair, M., Gordon, T.F., Walton, D.: Probabilistic semantics for the Carneades argument model using bayesian networks. In: Proc. of the 3rd Int. Conf. on Computational Models of Argument (COMMA 2010), Frontiers in Artificial Intelligence and Applications, vol. 216, pp. 255-266. IOS Press (2010)
[24] Haenni, R, Probabilistic argumentation, J. Appl. Log., 7, 155-176, (2009) · Zbl 1183.68617
[25] Hepler, AB; Dawid, P; Leucari, V, Object-oriented graphical representations of complex patterns of evidence, Law, Probability & Risk, 6, 275-293, (2007)
[26] Hinton, A., Kwiatkowska, M., Norman, G., Parker, D.: PRISM: A tool for automatic verification of probabilistic systems. In: Proc. of the 12th Int. Conf. on Tools and Algorithms for the Construction and Analysis of Systems (TACAS 2006), LNCS, vol. 3920, pp. 441-444. Springer-Verlag (2006) · Zbl 0877.68019
[27] Hunter, A, A probabilistic approach to modelling uncertain logical arguments, Int. J. Approx. Reason., 54, 47-81, (2013) · Zbl 1266.68176
[28] Hunter, A., Thimm, M.: Probabilistic argumentation with epistemic extensions. In: Proc. of the Int. Workshop on Defeasible and Ampliative Reasoning, vol. 1212. CEUR-WS.org (2014) · Zbl 1418.68193
[29] Hunter, A., Thimm, M.: Probabilistic argumentation with epistemic extensions and incomplete information. arXiv:1405.3376 (2014) · Zbl 0807.68085
[30] Hunter, A.: Thimm., M.: On partial information and contradictions in probabilistic abstract argumentation. In: Proc. of the 15th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR 2016), pp. 53-62 (2016)
[31] Jakobovits, H; Vermeir, D, Robust semantics for argumentation frameworks, J. Log. Comput., 9, 215-261, (1999) · Zbl 0933.68088
[32] Jech, T.: Set Theory, 3rd millennium edition, revised and expanded edn. Springer, Berlin (2003)
[33] Keppens, J, Argument diagram extraction from Bayesian networks, Artif. Intell. Law, 20, 109-143, (2012)
[34] Lam, H.P., Governatori, G., Riveret, R.: On ASPIC+ and Defeasible Logic. In: Proc. of the 6th Int. Conf. on Computational Models of Argument (COMMA 2016), Frontiers in Artificial Intelligence and Applications, vol. 287, pp. 359-370. IOS Press (2016)
[35] Li, H.: Probabilistic argumentation. Ph.D. thesis, Department of Computing Science, University of Aberdeen (2015)
[36] Li, H., Oren, N., Norman, T.J.: Probabilistic argumentation frameworks. In: Revised Selected Papers of the 1st Int. Workshop on Theory and Applications of Formal Argumentation (TAFA 2011), LNAI, vol. 7132, pp. 1-16. Springer (2011)
[37] Li, H., Oren, N., Norman, T.J.: Relaxing independence assumptions in probabilistic argumentation. In: Proc. of the 10th Int. Workshop on Argumentation in Multi-Agent Systems (2013)
[38] Liao, B., Huang, H.: Formulating semantics of probabilistic argumentation by characterizing subgraphs. In: Proc. of the 5th Int. Workshop on Logic, Rationality, and Interaction (LORI 2015), LNCS, vol. 9394, pp. 243-254. Springer (2015) · Zbl 06521582
[39] Liao, B., Xu, K., Huang, H.: Formulating semantics of probabilistic argumentation by characterizing subgraphs: Theory and empirical results. arXiv:1608.00302 (2016) · Zbl 1444.68184
[40] Modgil, S; Prakken, H, The ASPIC+ framework for structured argumentation: a tutorial, Argument & Computation, 5, 31-62, (2014)
[41] Nute, D.: Defeasible logic. In: Handbook of Logic in Artificial Intelligence and Logic Programming, pp. 353-395. Oxford University Press (2001)
[42] Oren, N., Norman, T.J.: Semantics for evidence-based argumentation. In: Proc. of the 2nd Int. Conf. on Computational Models of Argument (COMMA 2008), Frontiers in Artificial Intelligence and Applications, vol. 172, pp. 276-284. IOS Press (2008) · Zbl 0933.68088
[43] Polberg, S., Oren, N.: Revisiting support in abstract argumentation systems. In: Proc. of the 5th Int. Conf. on Computational Models of Argument (COMMA 2014), Frontiers in Artificial Intelligence and Applications, vol. 266, pp. 369-376. IOS Press (2014)
[44] Pollock, JL, Justification and defeat, Artif. Intell., 67, 377-407, (1994) · Zbl 0807.68085
[45] Pollock, J.L.: Cognitive Carpentry: A Blueprint for How to Build a Person. MIT Press, Cambridge (1995)
[46] Prakken, H.: On support relations in abstract argumentation as abstractions of inferential relations. In: Proc. of the 21st European Conf. on Artificial Intelligence (ECAI 2014), Frontiers in Artificial Intelligence and Applications, vol. 263, pp. 735-740. IOS Press (2014) · Zbl 1366.68294
[47] Prakken, H; Sartor, G, Argument-based extended logic programming with defeasible priorities, J. Appl. Non-Classical Log., 7, 25-75, (1997) · Zbl 0877.68019
[48] Rienstra, T.: Towards a probabilistic Dung-style argumentation system. In: Proc. of the 1st Int. Conf. on Agreement Technologies, vol. 918, pp. 138-152. CEUR (2012)
[49] Riveret, R., Governatori, G.: On learning attacks in probabilistic abstract argumentation. In: Proc. of the 15th Int. Conf. on Autonomous Agents &Multiagent Systems (AAMAS 2016), pp. 653-661. International Foundation for Autonomous Agents and Multiagent Systems (2016) · Zbl 1183.68617
[50] Riveret, R; Korkinof, D; Draief, M; Pitt, JV, Probabilistic abstract argumentation: an investigation with Boltzmann machines, Argument & Computation, 6, 178-218, (2015)
[51] Riveret, R., Pitt, J.V., Korkinof, D., Draief, M.: Neuro-symbolic agents: Boltzmann machines and probabilistic abstract argumentation with sub-arguments. In: Proc. of the14th Int. Conf. on Autonomous Agents and Multiagent Systems (AAMAS 2015), pp. 1481-1489. International Foundation for Autonomous Agents and Multiagent Systems (2015) · Zbl 1067.03038
[52] Riveret, R; Rotolo, A; Sartor, G, Probabilistic rule-based argumentation for norm-governed learning agents, Artif. Intell. Law, 20, 383-420, (2012) · Zbl 1297.68224
[53] Riveret, R., Rotolo, A., Sartor, G., Prakken, H., Roth, B.: Success chances in argument games: a probabilistic approach to legal disputes. In: Proc. of the 20th Conf. on Legal Knowledge and Information Systems (JURIX 2007), Frontiers in Artificial Intelligence and Applications, vol. 165, pp. 99-108. IOS Press (2007) · Zbl 1337.68241
[54] Roth, B., Riveret, R., Rotolo, A., Governatori, G.: Strategic argumentation: a game theoretical investigation. In: Proc. of the 11th Int. Conf. on Artificial Intelligence and Law (ICAIL 07), pp. 81-90. ACM (2007)
[55] Sato, T, A glimpse of symbolic-statistical modeling by PRISM, J. Intell. Inf. Syst., 31, 161-176, (2008)
[56] Sneyers, J., Meert, W., Vennekens, J., Kameya, Y., Sato, T.: Chr(prism)-based probabilistic logic learning. arXiv:1007.3858 (2010) · Zbl 1209.68100
[57] Sneyers, J; Schreye, DD; Fruhwirth, T, Probabilistic legal reasoning in chrism, Theory Pract. Logic Program., 13, 769-781, (2013) · Zbl 1286.68058
[58] Tang, Y., Oren, N., Sycara, K.P.: Markov argumentation random fields. In: Proc. of the 30th AAAI Conference on Artificial Intelligence (AAAI 2016), pp. 4397-4398. AAAI Press (2016)
[59] Thimm, M.: A probabilistic semantics for abstract argumentation. In: Proc. of the 20th European Conf. on Artificial Intelligence (ECAI 2012), Frontiers in Artificial Intelligence and Applications, vol. 242, pp. 750-755. IOS Press (2012) · Zbl 1327.68290
[60] Timmer, S.T., Meyer, J.J.C., Prakken, H., Renooij, S., Verheij, B.: Extracting legal arguments from forensic Bayesian networks. In: Proc. of the 27th Conf. on Legal Knowledge and Information Systems (JURIX 2014), Frontiers in Artificial Intelligence and Applications, vol. 271, pp. 71-80. IOS Press (2014)
[61] Timmer, S.T., Meyer, J.J.C., Prakken, H., Renooij, S., Verheij, B.: Explaining Bayesian networks using argumentation. In: Proc. of the 13th European Conf. on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2015), LNAI, vol. 9161, pp. 83-92. Springer (2015) · Zbl 06507006
[62] Timmer, S.T., Meyer, J.J.C., Prakken, H., Renooij, S., Verheij, B.: A structure-guided approach to capturing Bayesian reasoning about legal evidence in argumentation. In: Proc. of the 15th Int. Conf. on Artificial Intelligence and Law (ICAIL 2015), pp. 109-118 (2015) · Zbl 1331.68221
[63] Toni, F, A tutorial on assumption-based argumentation, Argument & Computation, 5, 89-117, (2014)
[64] Verheij, BF; Timmer, ST; Vlek, CS; Meyer, JJC; Renooij, S; Prakken, H, Arguments, scenarios and probabilities: connections between three normative frameworks for evidential reasoning, Law, Probability & Risk, 15, 35-70, (2015)
[65] Verheij, B.: Two approaches to dialectical argumentation: Admissible sets and argumentation stages. In: Proc. of the Int. Conf. on Formal and Applied Practical Reasoning (FAPR 1996), LNAI, vol. 1085, pp. 357-368. Springer (1996) · Zbl 1017.03511
[66] Verheij, B.: Jumping to conclusions - A logico-probabilistic foundation for defeasible rule-based arguments. In: Proc. of the 13th European Conf. on Logics in Artificial Intelligence (JELIA 2012), LNCS, vol. 7519, pp. 411-423. Springer (2012) · Zbl 1361.68244
[67] Verheij, B.: Arguments and their strength: Revisiting Pollock’s anti-probabilistic starting points. In: Proc. of the 5th Int. Conf. on Computational Models of Argument (COMMA 2014), Frontiers in Artificial Intelligence and Applications, vol. 266, pp. 433-444. IOS Press (2014)
[68] Verheij, B, To catch a thief with and without numbers: arguments, scenarios and probabilities in evidential reasoning, Law, Probability & Risk, 13, 307-325, (2014)
[69] Vreeswijk, G.A.W.: Argumentation in Bayesian belief networks. In: Revised Selected and Invited Papers of the 1st Int.Workshop on Argumentation in Multi-Agent Systems (ARGMAS 2004), LNCS, vol. 3366, pp. 111-129. Springer (2005) · Zbl 1211.68433
[70] Vreeswijk, G.A.W.: An algorithm to compute minimally grounded and admissible defence sets in argument systems. In: Proc. of the 1st Int. Conf. on Computational Models of Argument (COMMA 2006), Frontiers in Artificial Intelligence and Applications, vol. 144, pp. 109-120. IOS Press (2006)
[71] Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London (1991) · Zbl 0732.62004
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