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International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems

IPMU 2018: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations pp 736–748Cite as

First Steps Towards Harnessing Partial Functions in Fuzzy Type Theory

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 853))

Abstract

In this paper we present how the theory of partial functions can be developed in the fuzzy type theory and show how the theory elaborated by Lapierre [3] and Lepage [4] can be included in it. Namely, the latter is developed as a special theory whose models contain the partial functions in the sense introduced by both authors.

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Notes

  1. 1.

    It is required that Sq gives square root for all elements from \(M_{\epsilon }\), on which it is defined and may give arbitrary elements otherwise.

  2. 2.

    We silently assumed that the crisp inequality \(\ge \) is also defined.

  3. 3.

    In fact, we can consider here some arbitrary type \(\alpha \) provided that we will specify its properties characterizing people.

References

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

    Book  Google Scholar 

  2. Duží, M., Jespersen, B., Materna, P.: Procedural Semantics for Hyperintensional Logic. Springer, Dordrecht (2010). https://doi.org/10.1007/978-90-481-8812-3

    Book  MATH  Google Scholar 

  3. Lapierre, S.: A functional partial semantics for intensional logic. Notre Dame J. Formal Log. 33, 517–541 (1992)

    Article  MathSciNet  Google Scholar 

  4. Lepage, F.: Partial functions in type theory. Notre Dame J. Formal Log. 33, 493–516 (1992)

    Article  MathSciNet  Google Scholar 

  5. Novák, V.: On fuzzy type theory. Fuzzy Sets Syst. 149, 235–273 (2005)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Novák, V.: EQ-algebra-based fuzzy type theory and its extensions. Log. J. IGPL 19, 512–542 (2011)

    Article  MathSciNet  Google Scholar 

  8. Novák, V.: Towards fuzzy type theory with partial functions. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K.T., Krawczak, M. (eds.) IWIFSGN/EUSFLAT -2017. AISC, vol. 643, pp. 25–37. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-66827-7_3

    Chapter  Google Scholar 

  9. Novák, V.: Fuzzy type theory with partial functions. Iran. J. Fuzzy Syst. (submitted)

    Google Scholar 

  10. Tichý, P.: The Foundations of Frege’s Logic. De Gruyter, Berlin (1988)

    Book  Google Scholar 

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Acknowledgement

This paper was supported by the grant 16-19170S of GAČR, Czech Republic.

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Authors and Affiliations

  1. Institute for Research and Applications of Fuzzy Modeling, Centre of Excellence IT4Innovations, University of Ostrava, 30. dubna 22, 701 03, Ostrava 1, Czech Republic

    Vilém Novák

Authors
  1. Vilém Novák
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Correspondence to Vilém Novák .

Editor information

Editors and Affiliations

  1. Universidad de Cádiz, Cádiz, Cadiz, Spain

    Jesús Medina

  2. Universidad de Málaga, Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  3. Universidad de Granada, Granada, Spain

    José Luis Verdegay

  4. Universidad de Granada, Granada, Spain

    David A. Pelta

  5. Universidad de Málaga, Málaga, Málaga, Spain

    Inma P. Cabrera

  6. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, New York, USA

    Ronald R. Yager

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Novák, V. (2018). First Steps Towards Harnessing Partial Functions in Fuzzy Type Theory. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 853. Springer, Cham. https://doi.org/10.1007/978-3-319-91473-2_62

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  • DOI: https://doi.org/10.1007/978-3-319-91473-2_62

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91472-5

  • Online ISBN: 978-3-319-91473-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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