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 ∃Łukasiewicz 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.
Weierstrass approximations by Lukasiewicz formulas with one quantified variable / S. Aguzzoli, D. Mundici - In: 31st IEEE International Symposium on Multiple-Valued Logic : proceedings : 22-24 May 2001, Warsaw, PolandLos Alamitos : IEEE Computer Society Press, 2001. - ISBN 0769510833. - pp. 361-366 (( Intervento presentato al 31. convegno ISMVL’2001 tenutosi a Varsavia nel 2001.
Weierstrass approximations by Lukasiewicz formulas with one quantified variable
S. Aguzzoli;
2001
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 paper, ∃Ł is just infinite-valued ∃Łukasiewicz 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.Pubblicazioni consigliate
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