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What Is Fuzzy Natural Logic

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Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9376))

Abstract

Natural Logic. In 1970, G. Lakoff published a paper [8] in which he introduced the concept of natural logic with the following goals:

  • to express all concepts capable of being expressed in natural language,

  • to characterize all the valid inferences that can be made in natural language,

  • to mesh with adequate linguistic descriptions of all natural languages.

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References

  1. Andrews, P.: An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Kluwer, Dordrecht (2002)

    Book  MATH  Google Scholar 

  2. van Benthem, J.: A brief history of natural logic. In: Chakraborty, M., Löwe, B., Nath Mitra, M., Sarukkai, S. (eds.) Logic, Navya-Nyaya and Applications, Homage to Bimal Krishna Matilal. College Publications, London (2008)

    Google Scholar 

  3. Duží, M., Jespersen, B., Materna, P.: Procedural Semantics for Hyperintensional Logic. Springer, Dordrecht (2010)

    MATH  Google Scholar 

  4. Dvořák, A., Holčapek, M.: L-fuzzy quantifiers of the type \(\langle 1\rangle \) determined by measures. Fuzzy Sets and Systems 160, 3425–3452 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dvořák, A., Novák, V.: Formal theories and linguistic descriptions. Fuzzy Sets and Systems 143, 169–188 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hájek, P.: What is mathematical fuzzy logic. Fuzzy Sets and Systems 157, 597–603 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Holčapek, M.: Monadic L-fuzzy quantifiers of the type \(\langle 1^n, 1\rangle \). Fuzzy Sets and Systems 159, 1811–1835 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lakoff, G.: Linguistics and natural logic. Synthese 22, 151–271 (1970)

    Article  MATH  Google Scholar 

  9. MacCartney, B., Manning, C.D.: An extended model of natural logic. In: IWCS-8 1909 Proc. Eighth Int. Conf. on Computational Semantics, pp. 140–156. Association for Computational Linguistics, Stroudsburg, PA, USA (2009)

    Google Scholar 

  10. Murinová, P., Novák, V.: A formal theory of generalized intermediate syllogisms. Fuzzy Sets and Systems 186, 47–80 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. Murinová, P., Novák, V.: The structure of generalized intermediate syllogisms. Fuzzy Sets and Systems 247, 18–37 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  12. Novák, V.: On fuzzy type theory. Fuzzy Sets and Systems 149, 235–273 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Novák, V.: Perception-based logical deduction. In: Reusch, B. (ed.) Computational Intelligence, Theory and Applications, pp. 237–250. Springer, Berlin (2005)

    Chapter  Google Scholar 

  14. Novák, V.: Which logic is the real fuzzy logic? Fuzzy Sets and Systems 157, 635–641 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Novák, V.: Mathematical fuzzy logic in modeling of natural language semantics. In: Wang, P., Ruan, D., Kerre, E. (eds.) Fuzzy Logic - A Spectrum of Theoretical & Practical Issues, pp. 145–182. Elsevier, Berlin (2007)

    Google Scholar 

  16. Novák, V.: A comprehensive theory of trichotomous evaluative linguistic expressions. Fuzzy Sets and Systems 159(22), 2939–2969 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. Novák, V.: A formal theory of intermediate quantifiers. Fuzzy Sets and Systems 159(10), 1229–1246 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Novák, V.: EQ-algebra-based fuzzy type theory and its extensions. Logic Journal of the IGPL 19, 512–542 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Novák, V., Dvořák, A.: Formalization of commonsense reasoning in fuzzy logic in broader sense. Journal of Applied and Computational Mathematics 10, 106–121 (2011)

    MathSciNet  MATH  Google Scholar 

  20. Novák, V., Lehmke, S.: Logical structure of fuzzy IF-THEN rules. Fuzzy Sets and Systems 157, 2003–2029 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  21. Novák, V., Perfilieva, I.: On the semantics of perception-based fuzzy logic deduction. International Journal of Intelligent Systems 19, 1007–1031 (2004)

    Article  MATH  Google Scholar 

  22. Peterson, P.: Intermediate Quantifiers. Logic, linguistics, and Aristotelian semantics. Ashgate, Aldershot (2000)

    Google Scholar 

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Correspondence to Vilém Novák .

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Novák, V. (2015). What Is Fuzzy Natural Logic. In: Huynh, VN., Inuiguchi, M., Demoeux, T. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2015. Lecture Notes in Computer Science(), vol 9376. Springer, Cham. https://doi.org/10.1007/978-3-319-25135-6_3

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  • DOI: https://doi.org/10.1007/978-3-319-25135-6_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25134-9

  • Online ISBN: 978-3-319-25135-6

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