Skip to main content
SpringerLink
Log in

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

  • Conference paper
  • First Online:
Rough Sets and Current Trends in Computing (RSCTC 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1424))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Banerjee & M. Chakraborthy, Rough Sets Through Algebraic Logic. Fundamenta Informaticae, 28, 1996, pp. 211–221.

    MATH  MathSciNet  Google Scholar 

  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. 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. 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. 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. Z. Pawlak, Rough Sets: A Theoretical Approach to Reasoning about Data. Kluwer, 1991.

    Google Scholar 

  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. C. Rauszer, Semi-Boolean algebras and their application to intuitionistic logic with dual operations. Fundamenta Mathematicae LXXIII, 1974, pp. 219–249.

    MathSciNet  Google Scholar 

  9. G.E. Reyes & N. Zolfaghari, Bi-Heyting Algebras, Toposes and Modalities. Journ. of Philosophical Logic, 25, 1996, pp. 25–43.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Telecommunication Business Unit, FINSIEL-TELECOM, Via Bona, 65, 00156, Roma, Italy

    Piero Pagliani

Authors
  1. Piero Pagliani
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Mathematics, Warsaw University of Technology, Pl. Politechniki 1, 00-665, Warszawa, Poland

    Lech Polkowski

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warszawa, Poland

    Andrzej Skowron

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pagliani, P. (1998). Intrinsic Co-Heyting Boundaries and Information Incompleteness in Rough Set Analysis. In: Polkowski, L., Skowron, A. (eds) Rough Sets and Current Trends in Computing. RSCTC 1998. Lecture Notes in Computer Science(), vol 1424. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69115-4_18

Download citation

  • DOI: https://doi.org/10.1007/3-540-69115-4_18

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64655-6

  • Online ISBN: 978-3-540-69115-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation