Formal methods can strongly contribute to improve dependability of controllers during design, by providing means to avoid flaws due to designers' omissions or specifications misinterpretations. This paper presents a synthesis method dedicated to logic controllers. Its goal is to obtain the control laws from specifications given in natural language by symbolic computation. The formal framework that underlies this method is the Boolean algebra of n-variable switching functions. In this algebra, thanks to relations and theorems presented in this paper, it is possible to formally express logical controllers specifications, to automatically detect inconsistencies in specifications, and to obtain automatically the set of solutions or to choose an optimal solution according to given optimization criteria. The application of this synthesis method to an example allows illustrating its main advantages.