Skip to main content
SpringerLink
Log in

A Unified Formulation of Deduction, Induction and Abduction Using Granularity Based on VPRS Models and Measure-Based Semantics for Modal Logics

  • Chapter
Book cover Interval / Probabilistic Uncertainty and Non-Classical Logics

Part of the book series: Advances in Soft Computing ((AINSC,volume 46))

Summary

In this paper, we propose a unified formulation of deduction, induction and abduction using granularity based on variable precision rough set models proposed by Ziarko [12] and measure-based semantics for modal logics proposed by Murai et al. [4].

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 209.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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. Chellas, B.F.: Modal Logic: An Introduction. Cambridge University Press, Cambridge (1980)

    MATH  Google Scholar 

  2. Kudo, Y., Murai, T.: Approximation of Concepts and Reasoning Based on Rough Sets. Journal of Japanese Society for Artificial Intelligence 22(5), 597–604 (in Japanese, 2007)

    Google Scholar 

  3. Murai, T., Kudo, Y., Akama, S.: A Role of Granularity and Background Knowledge in Reasoning Processes — Towards a Foundation of Kansei Representation in Human Reasoning. Kansei Engineering International 6(3), 41–46 (2006)

    Google Scholar 

  4. Murai, T., Miyakoshi, M., Shimbo, M.: Measure-Based Semantics for Modal Logic. In: Fuzzy Logic: State of the Art, pp. 395–405. Kluwer, Dordrecht (1993)

    Google Scholar 

  5. Murai, T., Miyakoshi, M., Shimbo, M.: A Logical Foundation of Graded Modal Operators Defined by Fuzzy Measures. In: Proc. of 4th FUZZ-IEEE, pp. 151–156 (1995)

    Google Scholar 

  6. Murai, T., et al.: Granular Reasoning Using Zooming In & Out: Part 2. Aristotlefs Categorical Syllogism. Electronic Notes in Theoretical Computer Science 82(4) (2003)

    Google Scholar 

  7. Murai, T., et al.: Granular Reasoning Using Zooming In & Out: Part 1. Propositional Reasoning. In: Wang, G., et al. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 421–424. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  8. Pawlak, Z.: Rough Sets. International Journal of Computer and Information Science 11, 341–356 (1982)

    Article  MathSciNet  Google Scholar 

  9. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991)

    MATH  Google Scholar 

  10. Polkowski, L.: Rough sets: Mathematical Foundations. Advances in Soft Computing. Physica-Verlag (2002)

    Google Scholar 

  11. Yao, Y.Y., Wang, S.K.M., Lin, T.Y.: A Review of Rough Set Models. In: Rough Sets and Data Mining, pp. 47–75. Kluwer, Dordrecht (1997)

    Google Scholar 

  12. Ziarko, W.: Variable Precision Rough Set Model. Journal of Computer and System Science 46, 39–59 (1993)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Computer Science and Systems Eng., Muroran Institute of Technology, 27-1, Mizumoto, Muroran, 050-8585, Japan

    Yasuo Kudo

  2. Graduate School of Information Science and Technology, Hokkaido University, Kita 14, Nishi 9, Kita-ku, Sapporo, 060-0814, Japan

    Tetsuya Murai

  3. 1-20-1, Higashi-Yurigaoka, Asao-ku, Kawasaki 215-0012, Japan

    Seiki Akama

Authors
  1. Yasuo Kudo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tetsuya Murai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Seiki Akama
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Van-Nam Huynh Yoshiteru Nakamori Hiroakira Ono Jonathan Lawry Vkladik Kreinovich Hung T. Nguyen

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kudo, Y., Murai, T., Akama, S. (2008). A Unified Formulation of Deduction, Induction and Abduction Using Granularity Based on VPRS Models and Measure-Based Semantics for Modal Logics. In: Huynh, VN., Nakamori, Y., Ono, H., Lawry, J., Kreinovich, V., Nguyen, H.T. (eds) Interval / Probabilistic Uncertainty and Non-Classical Logics. Advances in Soft Computing, vol 46. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77664-2_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-77664-2_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77663-5

  • Online ISBN: 978-3-540-77664-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation