Skip to main content
SpringerLink
Log in
Book cover

Knowledge and Systems Engineering pp 327–338Cite as

Resolution in Linguistic Propositional Logic Based on Linear Symmetrical Hedge Algebra

  • Conference paper

  • 1023 Accesses

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 244))

Abstract

The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical hedge algebra. Then, we consider Gödel’s t-norm and t-conorm to define the logical connectives for our logic. Next, we present a resolution inference rule, in which two clauses having contradictory linguistic truth values can be resolved. We also give the concept of reliability in order to capture the approximative nature of the resolution inference rule. Finally, we propose a resolution procedure with the maximal reliability.

This is a preview of subscription content, 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   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
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. Ebrahim, R.: Fuzzy logic programming. Fuzzy Sets and Systems 117(2), 215–230 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. He, X., Liu, J., Xu, Y., Martínez, L., Ruan, D.: On -satisfiability and its -lock resolution in a finite lattice-valued propositional logic. Logic Journal of the IGPL 20(3), 579–588 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Lai, J., Xu, Y.: Linguistic truth-valued lattice-valued propositional logic system lp(x) based on linguistic truth-valued lattice implication algebra. Inf. Sci. 180(10), 1990–2002 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Le, V.H., Liu, F., Tran, D.K.: Fuzzy linguistic logic programming and its applications. TPLP 9(3), 309–341 (2009)

    MATH  Google Scholar 

  5. Lee, R.C.T.: Fuzzy logic and the resolution principle. In: IJCAI, pp. 560–567 (1971)

    Google Scholar 

  6. Mondal, B., Raha, S.: Approximate reasoning in fuzzy resolution. In: 2012 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), pp. 1–6 (2012)

    Google Scholar 

  7. Nguyenand, C.-H., Huynh, V.-N.: An algebraic approach to linguistic hedges in zadeh’s fuzzy logic. Fuzzy Sets and Systems 129(2), 229–254 (2002)

    Article  MathSciNet  Google Scholar 

  8. Nguyen, C.-H., Tran, D.-K., Huynh, V.-N., Nguyen, H.-C.: Hedge algebras, linguistic-valued logic and their application to fuzzy reasoning. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 7(4), 347–361 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. Nguyen, C.H., Wechler, W.: Hedge Algebras: An Algebraic Approach in Struture of Sets of Linguistic Truth Values. Fuzzy Sets and Syst. 35, 281–293 (1990)

    Article  MATH  Google Scholar 

  10. Phuong, L.A., Khang, T.D.: A deductive method in linguistic reasoning. In: 2012 2nd International Conference on Uncertainty Reasoning and Knowledge Engineering (URKE), pp. 137–140 (2012)

    Google Scholar 

  11. Phuong, L.A., Khang, T.D.: Linguistic reasoning based on generalized modus ponens with linguistic modifiers and hedge moving rules. In: 2012 International Conference on Fuzzy Theory and it’s Applications (iFUZZY), pp. 82–86 (2012)

    Google Scholar 

  12. Smutná, D., Vojtás, P.: Graded many-valued resolution with aggregation. Fuzzy Sets and Systems 143(1), 157–168 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  13. Vojtás, P.: Fuzzy logic programming. Fuzzy Sets and Systems 124(3), 361–370 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  14. Weigert, T.J., Tsai, J.J.P., Liu, X.: Fuzzy operator logic and fuzzy resolution. J. Autom. Reasoning 10(1), 59–78 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  15. Xu, Y., Ruan, D., Kerre, E.E., Liu, J.: Alpha-resolution principle based on lattice-valued propositional logic lp(x). Inf. Sci. 130(1-4), 195–223 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  16. Xu, Y., Ruan, D., Kerre, E.E., Liu, J.: Alpha-resolution principle based on first-order lattice-valued logic lf(x). Inf. Sci. 132(1-4), 221–239 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  17. Mukaidono, M., Shen, Z., Ding, L.: Fuzzy resolution principle. In: Proc. 18th Internat. Symp. on Multiple-valued Logic, pp. 210–215 (1989)

    Google Scholar 

  18. Zadeh, L.A.: Fuzzy sets. Information and Control 8(3), 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhong, X., Xu, Y., Liu, J., Chen, S.: General form of -resolution principle for linguistic truth-valued lattice-valued logic. Soft Comput. 16(10), 1767–1781 (2012)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Information Technology, Vinh University, Vinh, Vietnam

    Thi-Minh-Tam Nguyen

  2. School of Information and Communication Technology, Hanoi University of Science and Technology, Hanoi, Vietnam

    Viet-Trung Vu, The-Vinh Doan & Duc-Khanh Tran

Authors
  1. Thi-Minh-Tam Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Viet-Trung Vu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. The-Vinh Doan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Duc-Khanh Tran
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thi-Minh-Tam Nguyen .

Editor information

Editors and Affiliations

  1. School of Knowledge Science, Japan Advanced Institute of Science and Technology, Ishikawa, Japan

    Van Nam Huynh

  2. UMR CNRS 7253 Heudiasyc, Universite de Technologie de Compiegne, Compiegne Cedex, France

    Thierry Denoeux

  3. Faculty of Information Technology, Hanoi National University of Education, Hanoi, Vietnam

    Dang Hung Tran

  4. Faculty of Information Technology, University of Engineering and Technology, Hanoi, Vietnam

    Anh Cuong Le

  5. Faculty of Information Technology, University of Engineering and Technology, Hanoi, Vietnam

    Son Bao Pham

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Nguyen, TMT., Vu, VT., Doan, TV., Tran, DK. (2014). Resolution in Linguistic Propositional Logic Based on Linear Symmetrical Hedge Algebra. In: Huynh, V., Denoeux, T., Tran, D., Le, A., Pham, S. (eds) Knowledge and Systems Engineering. Advances in Intelligent Systems and Computing, vol 244. Springer, Cham. https://doi.org/10.1007/978-3-319-02741-8_28

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-02741-8_28

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02740-1

  • Online ISBN: 978-3-319-02741-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation