Rough Truth, Consequence, Consistency and Belief Revision

  • Mohua Banerjee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3066)


The article aims at re-visiting the notion of rough truth proposed by Pawlak in 1987 [11] and investigating some of its ‘logical’ consequences. We focus on the formal deductive apparatus \(\mathcal{L}_\mathcal{R}\) [12], that is sound and complete with respect to a semantics based on rough truth (extended to rough validity). The notion of rough consequence [4] is used in a modified form to formulate \(\mathcal{L}_\mathcal{R}\). The system has some desirable features of ‘rough’ reasoning – e.g. roughly true propositions can be derived from roughly true premisses in an information system. Further, rough consistency [4] is used to prove completeness. These properties of \(\mathcal{L}_\mathcal{R}\) motivate us to use it for a proposal of rough belief change. During change, the operative constraints on a system of beliefs are that of rough consistency preservation and deductive closure with respect to \(\mathcal{L}_\mathcal{R}\). Following the AGM [1] line, postulates for defining revision and contraction functions are presented. Interrelationships of these functions are also proved.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alchourrón, C., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet functions for contraction and revision. J. Symb. Logic 50, 510–530 (1985)zbMATHCrossRefGoogle Scholar
  2. 2.
    Banerjee, M., Chakraborty, M.K.: Rough consequence and rough algebra. In: Ziarko, W.P. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, Proc. Int. Workshop on Rough Sets and Knowledge Discovery (RSKD 1993), pp. 196–207. Springer, Heidelberg (1994)Google Scholar
  3. 3.
    Banerjee, M., Chakraborty, M.K.: Rough logics: a survey with further directions. In: Orłowska, E. (ed.) Incomplete Information: Rough Set Analysis, pp. 579–600. Springer, Heidelberg (1998)Google Scholar
  4. 4.
    Chakraborty, M.K., Banerjee, M.: Rough consequence. Bull. Polish Acad. Sc (Math.) 41(4), 299–304 (1993)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Gärdenfors, P., Rott, H.: Belief revision. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.) Handbook of Logic in AI and Logic Programming, Clarendon. Epistemic and Temporal Reasoning, vol. 4, pp. 35–132 (1995)Google Scholar
  6. 6.
    Gomolinska, A., Pearce, D.: Disbelief change. In: Sahlin, N.-E. (ed.) Spinning Ideas: Electronic Festschrift in Honour of P. Gärdenfors (2000),
  7. 7.
    Hughes, G.E., Cresswell, M.J.: A New Introduction to Modal Logic. Routledge (1996)Google Scholar
  8. 8.
    Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets: a tutorial. In: Pal, S.K., Skowron, A. (eds.) Rough Fuzzy Hybridization: A New Trend in Decision-Making, pp. 3–98. Springer, Heidelberg (1999)Google Scholar
  9. 9.
    Lepage, F., Lapierre, S.: Partial logic and the dynamics of epistemic states. In: Sahlin, N.-E. (ed.) Spinning Ideas: Electronic Festschrift in Honour of P. Gärdenfors (2000),
  10. 10.
    Pawlak, Z.: Rough sets. Int. J. Comp. Inf. Sci. 11, 341–356 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Pawlak, Z.: Rough logic. Bull. Polish Acad. Sc (Tech. Sc.) 35(5-6), 253–258 (1987)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Pawlak, Z., Banerjee, M.: A logic for rough truth (2004) (preprint)Google Scholar
  13. 13.
    Rott, H.: Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, Clarendon (2001)Google Scholar
  14. 14.
    Sahlin, N.-E. (ed.): Spinning Ideas: Electronic Festschrift in Honour of P. Gärdenfors (2000),
  15. 15.
    Studia Logica, Special Issue on Belief Revision, 73 (2003)Google Scholar
  16. 16.
    Wassermann, R.: Generalized change and the meaning of rationality postulates. Studia Logica 73, 299–319 (2003)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Mohua Banerjee
    • 1
  1. 1.Department of MathematicsIndian Institute of TechnologyKanpurIndia

Personalised recommendations