Skip to main content
SpringerLink
Log in

Theory of truth degrees of propositions in the logic system L * n

  • Published:
Science in China Series F: Information Sciences Aims and scope Submit manuscript

Abstract

By means of infinite product of uniformly distributed probability spaces of cardinal n the concept of truth degrees of propositions in the n-valued generalized Lukasiewicz propositional logic system L *n is introduced in the present paper. It is proved that the set consisting of truth degrees of all formulas is dense in [0, 1], and a general expression of truth degrees of formulas as well as a deduction rule of truth degrees is then obtained. Moreover, similarity degrees among formulas are proposed and a pseudo-metric is defined therefrom on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in n-valued generalized Lukasiewicz propositional logic is established.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Zadeh L A. Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans Systems, Man and Cybernet, 1973, 1: 28–44

    MathSciNet  Google Scholar 

  2. Dubois D, Prade H. Fuzzy sets in approximate reasoning. Fuzzy Sets and Systems, 1991, 40(1): 143–202

    Article  MATH  MathSciNet  Google Scholar 

  3. Pavelka J. On Fuzzy Logic I, II, III, Zeitschr. f. Math. Logik u. Grundlagen d. Math, 1979, 25: 45–52; 119–134; 447–464

    MATH  MathSciNet  Google Scholar 

  4. Ying M S. The fundamental theorem of ultroproduct in Pavelka’s logic. Z Math Logic Grundlagen Math, 1992, 38: 197–201

    MATH  MathSciNet  Google Scholar 

  5. Xu Y, Qin K Y, Liu J, et al. L-valued propositional logic Lvpl. Information Sciences, 1999, 144: 205–235

    MathSciNet  Google Scholar 

  6. Xu Y, Liu J, Song Z M, et al. On semantics of L-valued first order logic Lvfl. Int J General Systems, 2000, 29(1): 53–79

    MathSciNet  Google Scholar 

  7. Wang G J. On the logic foundation of fuzzy reasoning. Information Sciences, 1999, 117(1): 47–88

    Article  MATH  MathSciNet  Google Scholar 

  8. Hajek P. Metamathematics of Fuzzy Logic. Dordrecht: Kluwer Academic Publishers, 1998

    Google Scholar 

  9. Wang G J. Non-classic Logic and Approximate Reasoning (in Chinese). Beijing: Science Press, 2000

    Google Scholar 

  10. Ying M S. A logic for approximate reasoning. J Symbolic Logic, 1994, 59: 830–837

    Article  MATH  MathSciNet  Google Scholar 

  11. Wang G J, Chin K S, Dang C Y. A unified approximate reasoning theory suitable for propositional calculus system L* and predicate calculus system K*. Sci China Ser F-Inf Sci, 2005, 48(1): 1–14

    Article  MathSciNet  Google Scholar 

  12. Wang G J, Wang W. Logical metric spaces (in Chinese), Acta Math Sin, 2001, 44(1): 159–168

    MATH  Google Scholar 

  13. Wang G J, Fu L, Song J S. Theory of truth degrees of propositions in two-valued logic. Sci China Ser A-Math, 2002, 45(9): 1106–1116

    MathSciNet  Google Scholar 

  14. Halmos P R. Measure Theory, New York: Spring-Verlag, 1974

    Google Scholar 

  15. Adams EW. A Primer of Probability Logic, Stanford: CSLI Publications, 1998

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Shaanxi Normal University, Xi’an, 710062, China

    Li Jun & Wang Guojun

  2. School of Sciences, Lanzhou University of Technology, Lanzhou, 730050, China

    Li Jun

  3. Research Center for Science, Xi’an Jiaotong University, Xi’an, 710049, China

    Wang Guojun

Authors
  1. Li Jun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wang Guojun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Li Jun.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, J., Wang, G. Theory of truth degrees of propositions in the logic system L * n . SCI CHINA SER F 49, 471–483 (2006). https://doi.org/10.1007/s11432-006-2001-y

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-006-2001-y

Keywords

Search

Navigation