Skip to main content
SpringerLink
Log in

The Rough Logic and Roughness of Logical Theories

  • Conference paper
Rough Sets and Knowledge Technology (RSKT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4062))

Included in the following conference series:

  • 749 Accesses

Abstract

Tuples in an information system are taken as terms in a logical system, attributes as function symbols, a tuple taking a value at an attribute as an atomic formula. In such a way, an information system is represented by a logical theory in a logical language. The roughness of an information system is represented by the roughness of the logical theory, and the roughness of logical theories is a generalization of that of information systems. A logical theory induces an indiscernibility relation on the Herbrand universe of the logical language, the set of all the ground terms. It is imaginable that there is some connection between the logical implication of logical theories and the refinement of indiscernibility relations induced by the logical theories. It shall be proved that there is no such a connection of simple form.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Düntsch, I.: A logic for rough sets. Theoretical Computer Science 179, 427–436 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  2. Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets: a tutorial. In: Pal, S.K., Skowron, A. (eds.) Rough Fuzzy Hybridization: A New Trends in Decision-making, pp. 3–98. Springer, Heidelberg (1999)

    Google Scholar 

  3. Hájek, P.: Basic fuzzy logic and BL-algebras. Soft Computing 2, 124–128 (1998)

    Google Scholar 

  4. Hughes, G., Cresswell, M.: A new introduction to modal logic. Routledge, London (1996)

    Book  MATH  Google Scholar 

  5. Haack, S.: Deviant logic, fuzzy logic, beyond the formalism. The University of Chicago Press (1996)

    Google Scholar 

  6. Liau, C.: An overview of rough set semantics for modal and quantifier logics. International J. of Uncertainty, Fuzziness and Knowledge-Based Systems 8, 93–118 (2000)

    MATH  MathSciNet  Google Scholar 

  7. Pawlak, Z.: Rough sets - theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht (1991)

    MATH  Google Scholar 

  8. Pawlak, Z.: Rough sets, rough function and rough calculus. In: Pal, S.K., Skowron, A. (eds.) Rough Fuzzy Hybridization: A New Trends in Decision-making, pp. 99–109. Springer, Heidelberg (1999)

    Google Scholar 

  9. Pomykala, J., Pomykala, J.A.: The Stone algebra of rough sets. Bull. Polish Acad. Sci. Math. 36, 495–508 (1988)

    MATH  MathSciNet  Google Scholar 

  10. Yao, Y.Y., Wong, S.K.M., Lin, T.Y.: A review of rough set models. In: Lin, T.Y., Cercone, N. (eds.) Rough sets and data mining: analysis for imprecise data, pp. 47–75. Kluwer Academic Pub., Dordrecht (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, 100080, China

    Cungen Cao & Yuefei Sui

  2. Department of Computer Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu, 212003, China

    Zaiyue Zhang

Authors
  1. Cungen Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuefei Sui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zaiyue Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. College of Computer Science and Technology, Chongqing, University of Posts and Telecommunication, 400065, Chongqing, P.R. China

    Guo-Ying Wang

  2. Department of Electrical and Computer Engineering, University of Manitoba, R3T 5V6, Winnipeg, Manitoba, Canada

    James F. Peters

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

    Andrzej Skowron

  4. Department of Computer Science, University of Regina, Regina,, S4S 0A2, Saskatchewan, Canada

    Yiyu Yao

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cao, C., Sui, Y., Zhang, Z. (2006). The Rough Logic and Roughness of Logical Theories. In: Wang, GY., Peters, J.F., Skowron, A., Yao, Y. (eds) Rough Sets and Knowledge Technology. RSKT 2006. Lecture Notes in Computer Science(), vol 4062. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11795131_89

Download citation

  • DOI: https://doi.org/10.1007/11795131_89

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36297-5

  • Online ISBN: 978-3-540-36299-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation