Weierstrass approximations by Lukasiewicz formulas with one quantified variable

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 paper, ∃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