Algorithm for the automatic generation of a logical formula representing a control law

Given a continuous control function f we present an approximation algorithm for f, based on McNaughton's representation of propositions in the infinite-valued calculus of Lukasiewicz. Our algorithm outputs a formula belonging to a fragment of the Esteva-Godo-Montagna logic LΠ 1/2 ; this formula, on the one hand represents the human expert's approximate description of f, and on the other hand describes a function telling us, for every pair x, y in the phase space of the system, how much the output value y is appropriate for the input value x. We discuss the relevance of the algorithm for the general problems of fuzzy control.