Abstract
In real-world applications, knowledge bases consisting of all the information at hand for a specific domain, along with the current state of affairs, are bound to contain contradictory data coming from different sources, as well as data with varying degrees of uncertainty attached. Likewise, an important aspect of the effort associated with maintaining knowledge bases is deciding what information is no longer useful; pieces of information (such as intelligence reports) may be outdated, may come from sources that have recently been discovered to be of low quality, or abundant evidence may be available that contradicts them. In this paper, we propose a probabilistic structured argumentation framework that arises from the extension of Presumptive Defeasible Logic Programming (PreDeLP) with probabilistic models, and argue that this formalism is capable of addressing the basic issues of handling contradictory and uncertain data. Then, to address the last issue, we focus on the study of non-prioritized belief revision operations over probabilistic PreDeLP programs. We propose a set of rationality postulates – based on well-known ones developed for classical knowledge bases – that characterize how such operations should behave, and study a class of operators along with theoretical relationships with the proposed postulates, including a representation theorem stating the equivalence between this class and the class of operators characterized by the postulates.
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Martinez, M.V., García, A.J., Simari, G.R.: On the use of presumptions in structured defeasible reasoning. In: Proc. of COMMA, pp. 185–196 (2012)
Hansson, S.: Semi-revision. J. of App. Non-Classical Logics 7(1-2), 151–175 (1997)
Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: Partial meet contraction and revision functions. J. Sym. Log. 50(2), 510–530 (1985)
Gardenfors, P.: Knowledge in flux: Modeling the dynamics of epistemic states. MIT Press, Cambridge (1988)
Hansson, S.O.: Kernel contraction. J. Symb. Log. 59(3), 845–859 (1994)
Doyle, J.: A truth maintenance system. Artif. Intell. 12(3), 231–272 (1979)
Falappa, M.A., Kern-Isberner, G., Simari, G.R.: Explanations, belief revision and defeasible reasoning. Artif. Intell. 141(1/2), 1–28 (2002)
Li, H., Oren, N., Norman, T.J.: Probabilistic argumentation frameworks. In: Proc. of TAFA, pp. 1–16 (2011)
Thimm, M.: A probabilistic semantics for abstract argumentation. In: Proc. of ECAI 2012, pp. 750–755 (2012)
Hunter, A.: Some foundations for probabilistic abstract argumentation. In: Proc. of COMMA 2012, pp. 117–128 (2012)
Fazzinga, B., Flesca, S., Parisi, F.: On the complexity of probabilistic abstract argumentation. Proc. of IJCAI 2013 (2013)
Haenni, R., Kohlas, J., Lehmann, N.: Probabilistic argumentation systems. Springer (1999)
Chesñevar, C.I., Simari, G.R., Alsinet, T., Godo, L.: A logic programming framework for possibilistic argumentation with vague knowledge. In: Proc. of UAI 2004, pp. 76–84 (2004)
Hunter, A.: A probabilistic approach to modelling uncertain logical arguments. Int. J. Approx. Reasoning 54(1), 47–81 (2013)
Gottlob, G., Lukasiewicz, T., Martinez, M.V., Simari, G.I.: Query answering under probabilistic uncertainty in Datalog+/– ontologies. AMAI (2013)
Nilsson, N.J.: Probabilistic logic. Artif. Intell. 28(1), 71–87 (1986)
Khuller, S., Martinez, M.V., Nau, D.S., Sliva, A., Simari, G.I., Subrahmanian, V.S.: Computing most probable worlds of action probabilistic logic programs: Scalable estimation for 1030,000 worlds. AMAI 51(2-4), 295–331 (2007)
Simari, G.I., Martinez, M.V., Sliva, A., Subrahmanian, V.S.: Focused most probable world computations in probabilistic logic programs. AMAI 64(2-3), 113–143 (2012)
Rahwan, I., Simari, G.R.: Argumentation in Artificial Intelligence. Springer (2009)
García, A.J., Simari, G.R.: Defeasible logic programming: An argumentative approach. TPLP 4(1-2), 95–138 (2004)
Lloyd, J.W.: Foundations of Logic Programming, 2nd edn. Springer (1987)
Simari, G.R., Loui, R.P.: A mathematical treatment of defeasible reasoning and its implementation. Artif. Intell. 53(2-3), 125–157 (1992)
Stolzenburg, F., García, A., Chesñevar, C.I., Simari, G.R.: Computing Generalized Specificity. Journal of Non-Classical Logics 13(1), 87–113 (2003)
Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell. 77, 321–357 (1995)
Falappa, M.A., Kern-Isberner, G., Reis, M., Simari, G.R.: Prioritized and non-prioritized multiple change on belief bases. J. Philosophical Logic 41(1), 77–113 (2012)
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Shakarian, P., Simari, G.I., Falappa, M.A. (2014). Belief Revision in Structured Probabilistic Argumentation. In: Beierle, C., Meghini, C. (eds) Foundations of Information and Knowledge Systems. FoIKS 2014. Lecture Notes in Computer Science, vol 8367. Springer, Cham. https://doi.org/10.1007/978-3-319-04939-7_16
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DOI: https://doi.org/10.1007/978-3-319-04939-7_16
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