Advertisement

Intrinsic Co-Heyting Boundaries and Information Incompleteness in Rough Set Analysis

  • Piero Pagliani
Conference paper
  • 589 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1424)

Abstract

Probably the distinguishing concept in incomplete information analysis is that of “boundary”: in fact a boundary is precisely the region that represents those doubts arising from our information gaps. In the paper it is shown that the rough set analysis adequately and elegantly grasps this notion via the algebraic features provided by co-Heyting algebras.

Keywords

Boolean Algebra Approximation Space Heyting Algebra Stone Algebra Bounded Distributive Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Banerjee & M. Chakraborthy, Rough Sets Through Algebraic Logic. Fundamenta Informaticae, 28, 1996, pp. 211–221.zbMATHMathSciNetGoogle Scholar
  2. 2.
    P.T. Johnstone, Conditions related to De Morgan’s law. In M.P. Fourman, C.J. Mulvey & D. S. Scott (eds.), Applications of Sheaves (Durham 1977), LNM 753, Springer-Verlag, 1979, pp. 479–491.Google Scholar
  3. 3.
    F.W. Lawvere, Introduction to F. W. Lawvere & S. Schanuel (eds.), Categories in Continuum Physics (Buffalo 1982), LNM 1174, Springer-Verlag, 1986.Google Scholar
  4. 4.
    F. W. Lawvere, Intrinsic co-Heyting boundaries and the Leibniz rule in certain toposes. In A. Carboni, M.C. Pedicchio & G. Rosolini (eds.), Category Theory (Como 1990), LNM 1488, Springer-Verlag 1991, pp. 279–297.Google Scholar
  5. 5.
    E: Orłowska, Logic for reasoning about knowledge. In W.P. Ziarko (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, Springer-Verlag, 1994, pp. 227–236.Google Scholar
  6. 6.
    Z. Pawlak, Rough Sets: A Theoretical Approach to Reasoning about Data. Kluwer, 1991.Google Scholar
  7. 7.
    P. Pagliani, Rough Set System and Logic-algebraic Structures. In E. Orłowska (ed.): Incomplete Information: Rough Set Analysis, Physica Verlag, 1997, pp. 109–190.Google Scholar
  8. 8.
    C. Rauszer, Semi-Boolean algebras and their application to intuitionistic logic with dual operations. Fundamenta Mathematicae LXXIII, 1974, pp. 219–249.MathSciNetGoogle Scholar
  9. 9.
    G.E. Reyes & N. Zolfaghari, Bi-Heyting Algebras, Toposes and Modalities. Journ. of Philosophical Logic, 25, 1996, pp. 25–43.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Piero Pagliani
    • 1
  1. 1.Telecommunication Business UnitFINSIEL-TELECOMRomaItaly

Personalised recommendations