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 ŁUKASIEWICZ FORMULAS WITH ONE QUANTIFIED VARIABLE / D. MUNDICI; S. AGUZZOLI. - STAMPA. - (2001), pp. 361-366. ((Intervento presentato al convegno PROC. 31ST IEEE INT.SYMP. ON MULTIPLE VALUED LOGIC, ISMVL tenutosi a WARSAW, POLAND [10.1109/ISMVL.2001.924596].
WEIERSTRASS APPROXIMATIONS BY ŁUKASIEWICZ FORMULAS WITH ONE QUANTIFIED VARIABLE
MUNDICI, DANIELE;
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.
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