Logical Comparison of Inconsistent Perspectives using Scoring Functions Article

First Online: 06 February 2004 Received: 29 September 2001 Revised: 25 July 2002 Accepted: 26 February 2003 DOI :
10.1007/s10115-003-0125-6

Cite this article as: Hunter, A. Know. Inf. Sys. (2004) 6: 528. doi:10.1007/s10115-003-0125-6 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.

Keywords Conflict resolution Heterogeneous knowledge Inconsistency handling Logic-based negotiation

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

CrossRef 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

CrossRef 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

CrossRef Google Scholar 12.

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

CrossRef 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

CrossRef MathSciNet MATH Google Scholar 22.

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

CrossRef MathSciNet MATH Google Scholar 23.

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

CrossRef 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 Authors and Affiliations 1. Department of Computer Science University College London London UK