Weierstrass approximations by Lukasiewicz formulas with one quantified variable

Abstract

The logic /spl exist/L 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 /spl exist/L. As shown in this paper, /spl exist/L is just infinite-valued Lukasiewicz propositional logic with one quantified propositional variable. We evaluate the computational complexity of the decision problem for /spl exist/L. 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.