The logic There ExistsL of continuous piecewise linear functions with rational coefficients has enough expressive power to formalize Weier-strass approximation theorem. Thus, up to any prescribed error, every continuous (control) function can be approximated by a formula of There ExistsL. As shown in this work, There ExistsL is just infinite-valued Lukasiewicz propositional logic with one quantified propositional variable. We evaluate the computational complexity of the decision problem for There ExistsL 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.
Weierstrass approximation theorem and Łukasiewicz formulas with one quantified variable / D. MUNDICI; S. AGUZZOLI. - STAMPA. - (2003), pp. 315-335.
Weierstrass approximation theorem and Łukasiewicz formulas with one quantified variable
MUNDICI, DANIELE;
2003
Abstract
The logic There ExistsL of continuous piecewise linear functions with rational coefficients has enough expressive power to formalize Weier-strass approximation theorem. Thus, up to any prescribed error, every continuous (control) function can be approximated by a formula of There ExistsL. As shown in this work, There ExistsL is just infinite-valued Lukasiewicz propositional logic with one quantified propositional variable. We evaluate the computational complexity of the decision problem for There ExistsL 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.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.