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Weierstrass Approximation Theorem and Łukasiewicz Formulas with one Quantified Variable

  • Stefano Aguzzoli
  • Daniele Mundici
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 114)

Abstract

The logic ∃Ł of continuous piecewise linear functions with rational coefficients has enough expressive power to formalize Weierstrass approximation theorem. Thus, up to any prescribed error, every continuous (control) function can be approximated by a formula of ∃Ł. As shown in this work, ∃Ł is just infinite-valued Lukasiewicz propositional logic with one quantified propositional variable. We evaluate the computational complexity of the decision problem for ∃Ł. Enough background material is provided for all readers wishing to acquire a deeper understanding of the rapidly growing literature on Łukasiewicz propositional logic and its applications.

Keywords

Rational Coefficient Simplicial Complex Toric Variety Piecewise Linear Function Propositional Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Stefano Aguzzoli
    • 1
  • Daniele Mundici
    • 1
  1. 1.Department of Computer ScienceUniversity of MilanMilanItaly

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