Weierstrass approximation theorem and Łukasiewicz formulas with one quantified variable

  • Authors:

  • Stefano Aguzzoli;Daniele Mundici

  • Affiliations:

  • Department of Computer Science, University of Milan, Via Comelico 39-41, 20135 Milan, Italy;Department of Computer Science, University of Milan, Via Comelico 39-41, 20135 Milan, Italy

  • Venue:
  • Beyond two
  • Year:
  • 2003

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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 Lukasiewicz propositional logic and its applications.