Skip to main content

Weak Completeness of Resolution in a Linguistic Truth-Valued Propositional Logic

  • Chapter

Part of the book series: Advances in Soft Computing ((AINSC,volume 42))

Abstract

In the present paper, the weak completeness of a-resolution principle for a lattice-valued logic (L n ×L2)P(X) with truth value in a logical algebra ( lattice implication algebra L n ×L2, is established. Accordingly, the weak completeness of (Exactly, True)-resolution principle for a linguistic truth-valued propositional logic ℓ based on the linguistic truth-valued lattice implication algebra L-LIA is derived.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chen, S.W., Xu, Y., Ma, J.: A Linguistic Truth-Valued Uncertainty Reasoning Model Based on Lattice-Valued Logic. In: Wang, L., Jin, Y. (eds.) FSKD 2005. LNCS (LNAI), vol. 3613, pp. 276–284. Springer, Heidelberg (2005)

    Google Scholar 

  2. Herrera, F., Martínez, L.: A 2-Tuple Fuzzy Linguistic Representation Model for Computing With Words. IEEE Trans. Fuzzy Systems 8(6), 746–752 (2000)

    Article  Google Scholar 

  3. Ho, N.C., Wechler, W.: Hedge Algebras: An Algebraic Approach to Structure of Sets of Linguistic Truth Values. Fuzzy Sets and Systems 35, 281–293 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ho, N.C., Wechler, W.: Extended Hedge Algebras and Their Application to Fuzzy Logic. Fuzzy Sets and Systems 52, 259–281 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  5. Liu, J., et al.: A Lattice-Valued Linguistic-Based Decision-Making Method. In: Proc. of 2005 IEEE International Conference on Granular Computing, pp. 199–202. IEEE Computer Society Press, Los Alamitos (2005)

    Google Scholar 

  6. Ma, J., Chen, S., Xu, Y.: Fuzzy Logic from the Viewpoint of Machine Intelligence. Fuzzy Sets and Systems 157, 628–634 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer, Dordrecht (1999)

    MATH  Google Scholar 

  8. Novák, V.: Are Fuzzy Sets a Reasonable Tool for Modelling Vague Phenomena. Fuzzy Sets and Systems 156(3), 341–348 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Pei, Z., Xu, Y.: Lattice Implication Algebra Model of a Kind of Linguistic Terms and Its Inference. In: Proc. of the 6th International FLINS Conference, pp. 93–98 (2004)

    Google Scholar 

  10. Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach. Prentice-Hall, Englewood Cliffs (1995)

    MATH  Google Scholar 

  11. Truksen, I.B., Kandel, A., Zhang, Y.Q.: Universal Truth Tables and Normal Forms. IEEE Trans. Fuzzy Systems 6, 295–303 (1998)

    Article  Google Scholar 

  12. Truksen, I.B.: Computing with Descriptive and Verisic Words. In: Proc. of NAFIP’99, pp. 13–17 (2004)

    Google Scholar 

  13. Xu, Y., et al.: α- Resolution Principle Based on Lattice-Valued Propositional Logic LP(X). Information Sciences 130, 195–223 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  14. Xu, Y., et al.: Lattice-Valued Logic: An Alternative Approach to Treat Fuzziness and Incomparability. Springer, New York (2003)

    MATH  Google Scholar 

  15. Xu, Y., et al.: On the Consistency of Rule Bases Based on Lattice-Valued First-Order Logic LF(X). Int. J. Intelligent Systems 21, 399–424 (2006)

    Article  MATH  Google Scholar 

  16. Xu, Y., Chen, S.W., Ma, J.: Linguistic Truth-Valued Lattice Implication Algebra and Its Properties. In: Proc. CESA’06 (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Oscar Castillo Patricia Melin Oscar Montiel Ross Roberto Sepúlveda Cruz Witold Pedrycz Janusz Kacprzyk

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Xu, Y., Chen, S., Liu, J., Ruan, D. (2007). Weak Completeness of Resolution in a Linguistic Truth-Valued Propositional Logic. In: Castillo, O., Melin, P., Ross, O.M., Sepúlveda Cruz, R., Pedrycz, W., Kacprzyk, J. (eds) Theoretical Advances and Applications of Fuzzy Logic and Soft Computing. Advances in Soft Computing, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72434-6_36

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-72434-6_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72433-9

  • Online ISBN: 978-3-540-72434-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics