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A quantitative approach to belief revision in structured probabilistic argumentation

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Abstract

Many real-world knowledge-based systems must deal with information coming from different sources that invariably leads to incompleteness, overspecification, or inherently uncertain content. The presence of these varying levels of uncertainty doesn’t mean that the information is worthless – rather, these are hurdles that the knowledge engineer must learn to work with. In this paper, we continue work on an argumentation-based framework that extends the well-known Defeasible Logic Programming (DeLP) language with probabilistic uncertainty, giving rise to the Defeasible Logic Programming with Presumptions and Probabilistic Environments (DeLP3E) model. Our prior work focused on the problem of belief revision in DeLP3E, where we proposed a non-prioritized class of revision operators called AFO (Annotation Function-based Operators) to solve this problem. In this paper, we further study this class and argue that in some cases it may be desirable to define revision operators that take quantitative aspects into account, such as how the probabilities of certain literals or formulas of interest change after the revision takes place. To the best of our knowledge, this problem has not been addressed in the argumentation literature to date. We propose the QAFO (Quantitative Annotation Function-based Operators) class of operators, a subclass of AFO, and then go on to study the complexity of several problems related to their specification and application in revising knowledge bases. Finally, we present an algorithm for computing the probability that a literal is warranted in a DeLP3E knowledge base, and discuss how it could be applied towards implementing QAFO-style operators that compute approximations rather than exact operations.

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References

  1. 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)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alchourrón, C.E., Makinson, D.: On the logic of theory change: Contraction functions and their associated revision functions. Theoria 48(1), 14–37 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  3. Capobianco, M., Chesñevar, C.I., Simari, G.R.: Argumentation and the dynamics of warranted beliefs in changing environments. Intl. Journal on Autonomous Agents and Multiagent Systems (JAAMAS) 11, 127–151 (2005)

    Article  Google Scholar 

  4. Cecchi, L.A., Simari, G.R.: El marcado de un árbol dialéctico en DeLP es PSPACE-completo. In: Proceeding of Congreso Argentino de Ciencias de la Computación (CACIC) (2011)

  5. Chesñevar, C.I., Simari, G.R., Alsinet, T., Godo, L.: A logic programming framework for possibilistic argumentation with vague knowledge. In: Proceeding of UAI 2004, pp 76–84 (2004)

  6. Chvátal, V.: Linear programming. W.H.Freeman, New York (1983)

    MATH  Google Scholar 

  7. Dalal, M.: Investigations into a theory of knowledge base revision: Preliminary report. In: Proceeding of AAAI, pp 475–479 (1988)

  8. Deagustini, C.A.D., Martinez, M.V., Falappa, M.A., Simari, G.R.: Improving inconsistency resolution by considering global conflicts. In: Proceedings of SUM, pp. 120–133 (2014)

  9. Deagustini, C.A.D., Martinez, M.V., Falappa, M.A., Simari, G.R.: Inconsistency resolution and global conflicts. In: Proceedings of ECAI, pp. 991–992 (2014)

  10. Doyle, J.: A truth maintenance system. Artif. Intell. 12(3), 231–272 (1979)

    Article  MathSciNet  Google Scholar 

  11. 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)

    Article  MathSciNet  MATH  Google Scholar 

  12. Fagin, R., Halpern, J.Y., Megiddo, N.: A logic for reasoning about probabilities. Inf. Comput. 87(1/2), 78–128 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  13. Falappa, M.A., Garcia, A.J., Kern-Isberner, G., Simari, G.R.: On the evolving relation between belief revision and argumentation. Knowl. Eng. Rev. 26(01), 35–43 (2011)

    Article  Google Scholar 

  14. Falappa, M.A., Kern-Isberner, G., Simari, G.R.: Explanations, belief revision and defeasible reasoning. Artif. Intell. 141(1/2), 1–28 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  15. Falappa, M.A., Kern-Isberner, G., Simari, G.R.: Belief revision and argumentation theory. In: Argumentation in artificial intelligence, pp 341–360. Springer (2009)

  16. Fazzinga, B., Flesca, S., Parisi, F.: On the complexity of probabilistic abstract argumentation. In: Proceeding of IJCAI 2013 (2013)

  17. García, A.J., Simari, G.R.: Defeasible logic programming: an argumentative approach. TPLP 4(1-2), 95–138 (2004)

    MathSciNet  MATH  Google Scholar 

  18. Gardenfors, P.: Knowledge in flux: modeling the dynamics of epistemic states. MIT Press, Cambridge (1988)

    MATH  Google Scholar 

  19. Garey, M., Johnson, D.: Computers and intractability: a guide to the theory of NP-completeness. Freeman, New York (1979)

    MATH  Google Scholar 

  20. Gottlob, G., Lukasiewicz, T., Martinez, M.V., Simari, G.I.: Query answering under probabilistic uncertainty in Datalog +/−ontologies. AMAI (2013)

  21. Haenni, R., Kohlas, J., Lehmann, N.: Probabilistic argumentation systems. Springer (1999)

  22. Hansson, S.: Semi-revision. J. App. Non-Classical Logics 7(1-2), 151–175 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  23. Hansson, S.O.: Kernel contraction. J. Symb. Log. 59(3), 845–859 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  24. Hunter, A.: Some foundations for probabilistic abstract argumentation. In: Proceeding of COMMA 2012, pp 117–128 (2012)

  25. Hunter, A.: A probabilistic approach to modelling uncertain logical arguments. Int. J. Approx. Reasoning 54(1), 47–81 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  26. 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 10 30,000 worlds. AMAI 51(2-4), 295–331 (2007)

    MathSciNet  MATH  Google Scholar 

  27. Krause, P., Ambler, S., Elvang-Gørannson, M., Fox, J.: A logic of argumentation for reasoning under uncertainty. Comput. Intell. 11(1), 113–131 (1995)

    Article  MathSciNet  Google Scholar 

  28. Li, H., Oren, N., Norman, T.J.: Probabilistic argumentation frameworks. In: Proceeding of TAFA, pp 1–16 (2011)

  29. Lloyd, J.W.: Foundations of logic programming, 2nd edn. Springer (1987)

  30. Makinson, D.: On the status of the postulate of recovery in the logic of theory change. J. Philos. Log. 16(4), 383–394 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  31. Martinez, M.V., García, A.J., Simari, G.R.: On the use of presumptions in structured defeasible reasoning. In: Proceeding of COMMA, pp 185–196 (2012)

  32. Nilsson, N.J.: Probabilistic logic. Artif. Intell. 28(1), 71–87 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  33. Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference (1988)

  34. Poole, D.: The independent choice logic for modelling multiple agents under uncertainty. Artif. Intell. 94(1-2), 7–56 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  35. Rahwan, I., Simari, G.R.: Argumentation in artificial intelligence. Springer (2009)

  36. Richardson, M., Domingos, P.: Markov logic networks. Mach. Learn. 62, 107–136 (2006)

    Article  Google Scholar 

  37. Shakarian, P., Shakarian, J., Ruef, A.: Introduction to cyber-warfare: a multidisciplinary approach. Syngress (2013)

  38. Shakarian, P., Simari, G.I., Falappa, M.A.: Belief revision in structured probabilistic argumentation. In: Proceeding of FoIKS 2014, pp 324–343

  39. Shakarian, P., Simari, G.I., Moores, G., Parsons, S., Falappa, M.A.: An argumentation-based framework to address the attribution problem in cyber-warfare. In: Proceeding of Cyber Security 2014 (2014)

  40. Shakarian, P., Simari, G.I., Moores, G., Paulo, D., Parsons, S., Falappa, M.A., Aleali, A.: Belief revision in structured probabilistic argumentation: Model and application to cyber security. Under review (2014)

  41. Simari, G.R., Loui, R.P.: A mathematical treatment of defeasible reasoning and its implementation. Artif. Intell. 53(2-3), 125–157 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  42. Spohn, W.: The laws of belief: ranking theory and its philosophical applications. Oxford University Press (2012)

  43. Stolzenburg, F., García, A., Chesñevar, C.I., Simari, G.R.: Computing generalized specificity. J. Non-Classical Logics 13(1), 87–113 (2003)

    Article  MATH  Google Scholar 

  44. Thimm, M.: A probabilistic semantics for abstract argumentation. In: Proceeding of ECAI 2012, pp 750–755 (2012)

  45. Thimm, M.: Inconsistency measures for probabilistic logics. Artif. Intell. 197, 1–24 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  46. Toda, S.: On the computational power of PP and ⊕P. In: Proceeding of FOCS, pp 514–519 (1989)

  47. Wirth, C., Stolzenburg, F.: David Poole’s specificity revised. In: Proceeding of KR (2014)

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Universidad Nacional del Sur (UNS) and Institute for Computer Science and Engineering (CONICET-UNS), Bahia Blanca, Argentina

    Gerardo I. Simari & Marcelo A. Falappa

  2. Arizona State University, Tempe, AZ, USA

    Paulo Shakarian

Authors
  1. Gerardo I. Simari
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  2. Paulo Shakarian
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  3. Marcelo A. Falappa
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Correspondence to Gerardo I. Simari.

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Simari, G.I., Shakarian, P. & Falappa, M.A. A quantitative approach to belief revision in structured probabilistic argumentation. Ann Math Artif Intell 76, 375–408 (2016). https://doi.org/10.1007/s10472-015-9476-4

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