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.
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Aguzzoli, S., Mundici, D. (2003). Weierstrass Approximation Theorem and Łukasiewicz Formulas with one Quantified Variable. In: Fitting, M., Orłowska, E. (eds) Beyond Two: Theory and Applications of Multiple-Valued Logic. Studies in Fuzziness and Soft Computing, vol 114. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1769-0_14
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DOI: https://doi.org/10.1007/978-3-7908-1769-0_14
Publisher Name: Physica, Heidelberg
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