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Reasoning with Uncertainty by Nmatrix–Metric Semantics

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Logic, Language, Information and Computation (WoLLIC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5110))

Abstract

Non-deterministic matrices, a natural generalization of many-valued matrices, are semantic structures in which the value assigned to a complex formula may be chosen non-deterministically from a given set of options. We show that by combining Nmatrices and preferential metric-based considerations, one obtains a family of logics that are useful for reasoning with uncertainty. We investigate the basic properties of these logics and demonstrate their usefulness in handling incomplete and inconsistent information.

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References

  1. Arenas, M., Bertossi, L., Chomicki, J.: Answer sets for consistent query answering in inconsistent databases. Theory and Practice of Logic Programming 3(4–5), 393–424 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Arieli, O.: Commonsense reasoning by distance semantics. In: Proc. TARK 2007, pp. 33–41 (2007)

    Google Scholar 

  3. Arieli, O.: Distance-based paraconsistent logics. International Journal of Approximate Reasoning (in press, 2008), doi:10.1016/j.ijar.2007.07.002

    Google Scholar 

  4. Arieli, O., Avron, A.: General patterns for nonmonotonic reasoning: from basic entailments to plausible relations. Logic Journal of the IGPL 8(2), 119–148 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Arieli, O., Denecker, M., Bruynooghe, M.: Distance semantics for database repair. Annals of Mathematics and Artificial Intelligence 50(3–4), 389–415 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Arieli, O., Zamansky, A.: Non-deterministic distance-based semantics. In: Proc. AGI 2008. Frontiers in Artificial Intelligence, vol. 171, pp. 39–50. IOS Press, Amsterdam (2008)

    Google Scholar 

  7. Arieli, O., Zamansky, A.: Some simplified forms of reasoning with distance-based entailments. In: Bergler, S. (ed.) Canadian AI 2008. LNCS (LNAI), vol. 5032, pp. 36–47. Springer, Heidelberg (2008)

    Google Scholar 

  8. Avron, A., Lev, I.: Non-deterministic multi-valued structures. Journal of Logic and Computation 15, 241–261 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ben Naim, J.: Lack of finite characterizations for the distance-based revision. In: Proc. KR 2006, pp. 239–248 (2006)

    Google Scholar 

  10. Chomicki, J., Marchinkowski, J.: Minimal-change integrity maintenance using tuple deletion. Information and Computation 197(1–2), 90–121 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  11. Dalal, M.: Investigations into a theory of knowledge base revision. In: Proc. AAAI 1988, pp. 475–479. AAAI Press, Menlo Park (1988)

    Google Scholar 

  12. Gabbay, D.: Theoretical foundation for non-monotonic reasoning, Part II: Structured non-monotonic theories. In: Proc. SCAI 1991. IOS Press, Amsterdam (1991)

    Google Scholar 

  13. Gottwald, S.: A Treatise on Many-Valued Logics. Studies in Logic and Computation, vol. 9. Research Studies Press (2001)

    Google Scholar 

  14. Grove, A.: Two modellings for theory change. J. Phil. Logic 17, 157–180 (1988)

    MathSciNet  MATH  Google Scholar 

  15. Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44(1–2), 167–207 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  16. Lafage, C., Lang, J.: Propositional distances and preference representation. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 48–59. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  17. Lehmann, D., Magidor, M.: What does a conditional knowledge base entail? Artificial Intelligence 55, 1–60 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  18. Lehmann, D., Magidor, M., Schlechta, K.: Distance semantics for belief revision. Journal of Symbolic Logic 66(1), 295–317 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  19. Lopatenko, A., Bertossi, L.: Complexity of consistent query answering in databases under cardinality-based and incremental repair semantics. In: Schwentick, T., Suciu, D. (eds.) ICDT 2007. LNCS, vol. 4353, pp. 179–193. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  20. Makinson, D.: General patterns in nonmonotonic reasoning. In: Gabbay, D., Hogger, C., Robinson, J. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 35–110 (1994)

    Google Scholar 

  21. Pigozzi, G.: Two aggregation paradoxes in social decision making: the ostrogorski paradox and the discursive dilemma. Episteme 2(2), 33–42 (2005)

    Article  Google Scholar 

  22. Shoham, Y.: Reasoning about change. MIT Press, Cambridge (1988)

    Google Scholar 

  23. Spohn, W.: Ordinal conditional functions: a dynamic theory of epistemic states. In: Belief Change and Statistics, vol. II, pp. 105–134. Kluwer, Dordrecht (1988)

    Google Scholar 

  24. Tarski, A.: Introduction to Logic. Oxford University Press, Oxford (1941)

    Google Scholar 

  25. Urquhart, A.: Many-valued logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. II, pp. 249–295. Kluwer, Dordrecht (2001)

    Google Scholar 

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Wilfrid Hodges Ruy de Queiroz

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Arieli, O., Zamansky, A. (2008). Reasoning with Uncertainty by Nmatrix–Metric Semantics. In: Hodges, W., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2008. Lecture Notes in Computer Science(), vol 5110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69937-8_8

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  • DOI: https://doi.org/10.1007/978-3-540-69937-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69936-1

  • Online ISBN: 978-3-540-69937-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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