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Belief revision in structured probabilistic argumentation

Model and application to cyber security

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Abstract

In real-world applications, knowledge bases consisting of all the available information for a specific domain, along with the current state of affairs, will typically contain contradictory data, coming from different sources, as well as data with varying degrees of uncertainty attached. An important aspect of the effort associated with maintaining such knowledge bases is deciding what information is no longer useful; pieces of information may be outdated; may come from sources that have recently been discovered to be of low quality; or abundant evidence may be available that contradicts them.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 these basic issues. The formalism is capable of handling contradictory and uncertain data, and we study non-prioritized belief revision over probabilistic PreDeLP programs that can help with knowledge-base maintenance. For belief revision, we propose a set of rationality postulates — based on well-known ones developed for classical knowledge bases — that characterize how these belief revision operations should behave, and study classes of operators along with theoretical relationships with the proposed postulates, including representation theorems stating the equivalence between classes of operators and their associated postulates. We then demonstrate how our framework can be used to address the attribution problem in cyber security/cyber warfare.

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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. Altheide, C.: Digital Forensics with Open Source Tools. Syngress (2011)

  3. Bondarenko, A., Dung, P.M., Kowalski, R.A., Toni, F.: An abstract, argumentation-theoretic approach to default reasoning. Artif. Intell. 93(1), 63–101 (1997)

    Article  MathSciNet  MATH  Google Scholar 

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

  5. Corp., S.: Stuxnet 0.5: Disrupting Uranium Processing at Natanz. Symantec Connect (2013). http://www.symantec.com/connect/blogs/stuxnet-05-disrupting-uranium-processing-natanz

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

    Article  MathSciNet  Google Scholar 

  7. 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 

  8. Dunne, P.E., Hunter, A., McBurney, P., Parsons, S., Wooldridge, M.: Weighted argument systems: basic definitions, algorithms, and complexity results. Artif. Intell. 175(2), 457–486 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Falappa, M.A., García, A.J., Kern-Isberner, G., Simari, G.R.: On the evolving relation between belief revision and argumentation. Knowl. Eng. Rev. 26(1), 35–43 (2011). doi:10.1017/S0269888910000391

    Article  Google Scholar 

  10. 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)

    Article  MathSciNet  MATH  Google Scholar 

  11. 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 

  12. Falappa, M.A., Kern-Isberner, G., Simari, G.R.: Argumentation in artificial intelligence, chap. In: Rahwan, I., Simari, G.R. (eds.) Belief Revision and Argumentation Theory, pp 341–360. Springer (2009)

  13. Falliere, N., Murchu, L.O., Chien, E.: W32.Stuxnet Dossier Version 1.4. Symantec Corporation (2011)

  14. Fazzinga, B., Flesca, S., Parisi, F.: On the complexity of probabilistic abstract argumentation. In: Proceedings of IJCAI 2013, pp 898–904 (2013)

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

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  17. Gärdenfors, P.: Belief revision, vol. 29. Cambridge University Press (2003)

  18. Gottlob, G., Lukasiewicz, T., Martinez, M.V., Simari, G.I.: Query answering under probabilistic uncertainty in Datalog+/– ontologies. AMAI, 37–72 (2013)

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

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  22. Heuer, R.J.: Psychology of Intelligence Analysis. Center for the Study of Intelligence (1999). http://www.odci.gov/csi/books/19104/index.html

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

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

    Article  MathSciNet  MATH  Google Scholar 

  25. 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)

    MathSciNet  MATH  Google Scholar 

  26. 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 

  27. Langner, R.: Matching Langner Stuxnet analysis and Symantic dossier update. Langner Communications GmbH (2011). http://www.langner.com/

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

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

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

  31. Modgil, S., Prakken, H.: A general account of argumentation with preferences. Artif. Intell. 195, 361–397 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  33. Prakken, H.: An abstract framework for argumentation with structured arguments. Argument and Computation 1, 93–124 (2010)

    Article  Google Scholar 

  34. Rahwan, I., Simari, G.R.: Argumentation in Artificial Intelligence. Springer (2009)

  35. Richardson, M., Domingos, P.: Markov logic networks. Mach. Learn. 62(1–2), 107–136 (2006)

    Article  Google Scholar 

  36. Riley, L., Atkinson, K., Payne, T., Black, E.: An implemented dialogue system for inquiry and persuasion. In: Theory and Applications of Formal Argumentation, Lecture Notes in Computer Science, pp 67–84. Springer, Berlin (2011)

  37. Shadows in the Cloud: Investigating Cyber Espionage 2.0. Tech. rep., Information Warfare Monitor & Shadowserver Foundation (2010)

  38. Shafer, G., et al.: A mathematical theory of evidence, vol. 1. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  39. Shakarian, P., Shakarian, J., Ruef, A.: Introduction to Cyber-Warfare: A Multidisciplinary Approach. Syngress (2013)

  40. Shakarian, P., Simari, G.I., Falappa, M.A.: Belief revision in structured probabilistic argumentation. In: Proceedings of Foundations of Information and Knowledge Systems, pp 324–343 (2014)

  41. 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: Proceedings of Cyber Security (2014)

  42. 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)

    MathSciNet  MATH  Google Scholar 

  43. 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 

  44. Spitzner, L.: Honeypots: catching the insider threat. In: Proceedings of ACSAC 2003, pp 170–179. IEEE Computer Society (2003)

  45. 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 

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

  47. Thonnard, O., Mees, W., Dacier, M.: On a multicriteria clustering approach for attack attribution. SIGKDD Explor. 12(1), 11–20 (2010)

    Article  Google Scholar 

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Authors and Affiliations

  1. Arizona State University, Tempe, AZ, USA

    Paulo Shakarian & Ashkan Aleali

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

    Gerardo I. Simari & Marcelo A. Falappa

  3. Department of Electrical Engineering and Computer Science, U.S. Military Academy, West Point, NY, USA

    Geoffrey Moores & Damon Paulo

  4. Department of Computer Science, University of Liverpool, Liverpool, UK

    Simon Parsons

Authors
  1. Paulo Shakarian
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  2. Gerardo I. Simari
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  3. Geoffrey Moores
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  4. Damon Paulo
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  5. Simon Parsons
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  6. Marcelo A. Falappa
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  7. Ashkan Aleali
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Correspondence to Paulo Shakarian.

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Shakarian, P., Simari, G.I., Moores, G. et al. Belief revision in structured probabilistic argumentation. Ann Math Artif Intell 78, 259–301 (2016). https://doi.org/10.1007/s10472-015-9483-5

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