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Logical Comparison of Inconsistent Perspectives using Scoring Functions

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Abstract

The language for describing inconsistency is underdeveloped. If a database (a set of formulae) is inconsistent, there is usually no qualification of that inconsistency. Yet, it would seem useful to be able to say how inconsistent a database is, or to say whether one database is “more inconsistent” than another database. In this paper, we provide a more general characterization of inconsistency in terms of a scoring function for each database Δ. A scoring function S is from the power set of Δ into the natural numbers defined so that S(Γ) gives the number of minimally inconsistent subsets of Δ that would be eliminated if the subset Γ was removed from Δ. This characterization offers an expressive and succinct means for articulating, in general terms, the nature of inconsistency in a set of formulae. We then compare databases using their scoring functions. This gives an intuitive ordering relation over databases that we can describe as “more inconsistent than”. These techniques are potentially useful in a wide range of problems including monitoring progress in negotiations between a number of participants, and in comparing heterogeneous sources of information.

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References

  1. Benferhat S, Dubois D, Kaci S, Prade H (2000) Encoding information fusion in possibilistic logic: A general framework for rational syntactic merging. In Proc of the 14th Eur Conf on Artif Intell (ECAI’2000), IOS Press, pp 3–7

    MATH  Google Scholar 

  2. Benferhat S, Dubois D, Prade H (1993) Argumentative inference in uncertain and inconsistent knowledge bases. In Proc of the 9th Conf on Uncertainty in Artif Intell. Morgan Kaufmann, pp 411–419

  3. Brewka G (1989) Preferred subtheories: An extended logical framework for default reasoning. In Proc of the Eleventh Int Conf on Art Intell, pp 1043–1048

    Google Scholar 

  4. Cayrol C, Royer V, Saurel C (1993) Management of preferences in assumption based reasoning. In Inf Process and the Manage of Uncertainty in Knowledge based Syst (IPMU’92), Vol 682 of Lecture Notes in Comput Sci. Springer, Berlin Heidelberg New York

  5. Cholvy L (1995) Automated reasoning with merged contradictory information whose reliability depends on topics. In Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU’95), Vol 946 of Lecture Notes in Comput Sci. Springer, Berlin Heidelberg New York

  6. Dechter R, Pearl J (1987) Network-based heuristics for constraint-satisfaction problems. Artif Intell 34:1–38

    Article  MathSciNet  MATH  Google Scholar 

  7. Dubois D, Lang J, Prade H (1994) Possibilistic logic. In Handbook of Logic in Artificial Intelligence and Logic Programming, Vol 3, Oxford University Press, pp 439–513

  8. Elvang-Goransson M, Hunter A (1995) Argumentative logics: Reasoning from classically inconsistent information. Data Knowl Eng 16:125–145

    Article  Google Scholar 

  9. Gardenfors P (1988) Knowledge in Flux. MIT Press

  10. Garey M, Johnson D (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman

    Google Scholar 

  11. Hunter A, Nuseibeh B (1998) Managing inconsistent specifications: Reasoning, analysis and action. ACM Trans Softw Eng Methodol 7:335–367

    Article  Google Scholar 

  12. Kleer JD, Williams B (1987) Diagnosing multiple faults. Artif Intell 32:97–130

    Article  MATH  Google Scholar 

  13. Konieczny S, Pino Perez R (1998) On the logic of merging. In Proc of the Sixth Int Conf on Principles of Knowledge Representation and Reasoning (KR98). Morgan Kaufmann, pp 488–498

  14. Koriche F (2001) On anytime coherence-based reasoning. In Quantitative and Qualitative Approaches to Reasoning with Uncertainty (Ecsqaru’01), Vol 2143 of Lecture Notes in Comput Sci. Springer, Berlin Heidelberg New York, pp 544–556

  15. Levesque H (1984) A logic of implicit and explicit belief. In Proc of the National Conference on Artif Intell (AAAI’84), pp 198–202

  16. Lin J, Mendelzon A (1998) Merging databases under constraints. Int J Coop Inf Syst 7(1)

  17. Manor R, Rescher N (1970) On inferences from inconsistent information. Theory Decis 1:179–219

    MATH  Google Scholar 

  18. Oppacher F, Suen E (1988) HARP: A tableau-based theorem prover. J Autom Reasoning 4:69–100

    MathSciNet  Google Scholar 

  19. Papadimitriou C (1994) Computational Complexity. Addison-Wesley

  20. Papini O (2000) Knowledge-base revision. Knowl Eng Rev, pp 339–370

  21. Reiter R (1987) A theory of diagnosis from first principles. Artif Intell 32:57–95

    Article  MathSciNet  MATH  Google Scholar 

  22. Revesz P (1997) On the semantics of arbitration. Int J Algebra Comput 7:133–160

    Article  MathSciNet  MATH  Google Scholar 

  23. Schaerf M, Cadoli M (1995) Tractable reasoning via approximation. Artif Intell 74:249–310

    Article  MathSciNet  MATH  Google Scholar 

  24. Selman B, Levesque H, Mitchell D (1992) A new method for solving hard satisfiability problems. In Proc of the Tenth National Conf on Artif Intell (AAAI’92), pp 440–446

  25. Wong P, Besnard P (2001) Paraconsistent reasoning as an analytic tool. J Interest Group Propositional Logic 9:233–246

    Google Scholar 

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  1. Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, UK

    Anthony Hunter

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  1. Anthony Hunter
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Correspondence to Anthony Hunter.

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Hunter, A. Logical Comparison of Inconsistent Perspectives using Scoring Functions. Know. Inf. Sys. 6, 528–543 (2004). https://doi.org/10.1007/s10115-003-0125-6

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  • DOI: https://doi.org/10.1007/s10115-003-0125-6

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