Weierstrass Approximation Theorem and Łukasiewicz Formulas with one Quantified Variable
Stefano Aguzzoli, Daniele Mundici · Studies in fuzziness and soft computing · 2003
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. 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.