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On Vagueness, Truth Values and Fuzzy Logics

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Abstract

Some aspects of vagueness as presented in Shapiro’s book Vagueness in Context [23] are analyzed from the point of fuzzy logic. Presented are some generalizations of Shapiro’s formal apparatus.

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References

  1. Cignoli R.L.O., Esteva F., Godo L., Torrens A.: ‘Basic logic is the logic of continuous t-norms and thier residua’,. Soft Computing 4, 106–112 (2000)

    Article  Google Scholar 

  2. Cintula P.: ‘Weakly implicative (fuzzy) logics I: basic properties’,. Arch. Math. Logic 45, 673–704 (2006)

    Article  Google Scholar 

  3. Cornelis C., Deschrijver G., Kerre E.E.: ‘Advances and challenges in interval valued fuzzy logic’,. Fuzzy sets and systems 157, 622–627 (2006)

    Article  Google Scholar 

  4. Deschriever G., Cornelis C.: ‘Representability in interval-valued fuzzy set theory’,. Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems 15, 345–361 (2007)

    Article  Google Scholar 

  5. Edgington, D., ‘Vagueness by degrees’, in Keefe and Smith (eds.), Vagueness: A reader, MIT Cambridge Mass., 1997, pp. 294–316.

  6. Esteva F., Garcia-Calvés P., Godo L.: ‘Enriched interval bilattices and partial many-valued logics: an approach to deal with graded truth and imprecision’,. Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems 2, 37–54 (1994)

    Article  Google Scholar 

  7. Esteva F., Godo L.: ‘Monoidal t-norm based logic’,. Fuzzy sets and systems, 124, 271–288 (2001)

    Article  Google Scholar 

  8. Esteva F., Godo L., Montagna F.: ‘The ŁΠ and ŁΠ\({\frac12}\) logics: Two complete fuzzy systems joining Łukasiewicz and product logic’,. Arch. Math. Logic 40, 39–67 (2001)

    Article  Google Scholar 

  9. Fermúller C.G.: ‘Theories of vagueness versus fuzzy logic: can logicians learn from philosophers?’,. Neural Network World 13, 455–465 (2003)

    Google Scholar 

  10. Fine K.: ‘Vagueness, truth and logic’,. Synthese 30, 265–300 (1975)

    Article  Google Scholar 

  11. Gaifman, H., Vagueness, tolerance and contextual logic, Unpublished? Available from Gaifman’s web pages.

  12. Gerla, G., Fuzzy logic – mathematical tools for approximate reasoning, Kluwer, 2001.

  13. Giles, R., ‘Łukasiewicz Logic and Fuzzy Set Theory’, International Journal of Man-Machine Studies 313–327, 1976.

  14. van Gasse, B., C. Cornelis, D. Geschrijver, and E. E. Kerre, Triangle algebras: towards an axiomatization of interval-valued residuated lattices, RSCTC 06 Kobe, Japan.

  15. Hájek, P., Metamathematics of Fuzzy Logic, Kluwer, 1998.

  16. Hájek, P., ‘Fuzzy logic’. In Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/logic-fuzzy/

  17. Hájek P., Novák V.: ‘The Sorites paradox and fuzzy logic’,. Int. J. of General Systems 32, 373–383 (2003)

    Article  Google Scholar 

  18. Horčík R., Cintula P.: ‘Product Łukasiewicz logic’,. Arch. Math. Log. 43, 477–503 (2004)

    Article  Google Scholar 

  19. Keefe, R., Theories of Vagueness, Cambridge University Press, 2000.

  20. McGee V., McLaughlin B.: ‘Distinctions without difference’,. Southern Journal of Philosophy 33, 203–251 (1994)

    Article  Google Scholar 

  21. Mundici D.: ‘Bookmaking over infinite-valued events’,. International Journal of Approximate Reasoning 43, 223–240 (2006)

    Article  Google Scholar 

  22. Pavelka, J., ‘On fuzzy logic I, II, III’, Zeitschrift fúr Math. Logik und Grundlagen der Math. 25:45–52, 119–134, 447–464, 1979.

  23. Shapiro, S., Vagueness in Context, Oxford University Press, 2006.

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  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, Prague 8, Czech Republic

    Petr Hájek

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  1. Petr Hájek
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Hájek, P. On Vagueness, Truth Values and Fuzzy Logics. Stud Logica 91, 367–382 (2009). https://doi.org/10.1007/s11225-009-9179-0

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