Skip to main content
SpringerLink
Log in

Resolution in Linguistic First Order Logic Based on Linear Symmetrical Hedge Algebra

  • Conference paper
Book cover Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 442))

  • 919 Accesses

Abstract

This paper focuses on resolution in linguistic first order logic with truth value taken from linear symmetrical hedge algebra. We build the basic components of linguistic first order logic, including syntax and semantics. We present a resolution principle for our logic to resolve on two clauses having converse linguistic truth values. Since linguistic information is uncertain, inference in our linguistic logic is approximate. Therefore, we introduce the concept of reliability in order to capture the natural approximation of the resolution inference rule.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Chang, C.-L., Lee, R.C.-T.: Symbolic Logic and Mechanical Theorem Proving, 1st edn. Academic Press, Inc., Orlando (1997)

    Google Scholar 

  2. Ebrahim, R.: Fuzzy logic programming. Fuzzy Sets and Systems 117(2), 215–230 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Esteva, F., Godo, L., Noguera, C.: A logical approach to fuzzy truth hedges. Information Sciences 232, 366–385 (2013)

    Article  MathSciNet  Google Scholar 

  4. Ho, N.C., Wechler, W.: Extended hedge algebras and their application to fuzzy logic. Fuzzy Sets and Systems 52(3), 259 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  5. Háek, P.: On very true. Fuzzy Sets and Systems 124(3), 329 (2001)

    Article  MathSciNet  Google Scholar 

  6. Klement, E.P.: Some mathematical aspects of fuzzy sets: triangular norms, fuzzy logics, and generalized measures. Fuzzy Sets Syst. 90(2), 133–140 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Le, V.H., Liu, F., Tran, D.K.: Fuzzy linguistic logic programming and its applications. Theory Pract. Log. Program. 9(3), 309–341 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  8. Lee, R.C.T.: Fuzzy logic and the resolution principle. J. ACM 19(1), 109–119 (1972)

    Article  MATH  Google Scholar 

  9. 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 (August 2012)

    Google Scholar 

  10. 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)

    Google Scholar 

  11. Nguyen, T.-M.-T., Vu, V.-T., Doan, T.-V., Tran, D.-K.: Resolution in linguistic propositional logic based on linear symmetrical hedge algebra. In: Huynh, V.N., Denoeux, T., Tran, D.H., Le, A.C., Pham, B.S. (eds.) KSE 2013, Part I. AISC, vol. 244, pp. 337–350. Springer, Heidelberg (2014)

    Google Scholar 

  12. 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 

  13. 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 

  14. Robinson, J.A.: A machine-oriented logic based on the resolution principle. J. ACM 12(1), 23–41 (1965)

    Article  MATH  Google Scholar 

  15. Shen, Z., Ding, L., Mukaidono, M.: Fuzzy resolution principle. In: Proceedings of the Eighteenth International Symposium on Multiple-Valued Logic, pp. 210–215 (1988)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  17. Tran, D.-K., Vu, V.-T., Doan, T.-V., Nguyen, M.-T.: Fuzzy linguistic propositional logic based on refined hedge algebra. In: 2013 IEEE International Conference on Fuzzy Systems (FUZZ), pp. 1–8 (2013)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  19. Vychodil, V.: Truth-depressing hedges and bl-logic. Fuzzy Sets and Systems 157(15), 2074 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Vinh University, Vietnam

    Thi-Minh-Tam Nguyen

  2. Hanoi University of Science and Technology, Vietnam

    Viet-Trung Vu & The-Vinh Doan

  3. Vietnamese German University, Vietnam

    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

Editor information

Editors and Affiliations

  1. University Montpellier 2, LIRMM - CNRS UMR 5506, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Anne Laurent

  2. LIRMM, UMR CNRS/Universite Montpellier II, 161 rue Ada, 34392, Montpellier cedex 5, France

    Olivier Strauss

  3. LIP6, UPMC Univ. Paris 06, CNRS UMR 7606, F-75005, Paris, France

    Bernadette Bouchon-Meunier

  4. Dept. of Information Systems, Iona College, 710 North Ave, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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 First Order Logic Based on Linear Symmetrical Hedge Algebra. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 442. Springer, Cham. https://doi.org/10.1007/978-3-319-08795-5_36

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08795-5_36

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08794-8

  • Online ISBN: 978-3-319-08795-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation