We propose an original method for programming robots based on Bayesian inference and learning. This method formally deals with problems of uncertainty and incomplete information that are inherent to the field. Indeed, the principal difficulties of robot programming comes from the unavoidable incompleteness of the models used. We present the formalism for describing a robotic task as well as the resolution methods. This formalism is inspired by the theory of probability, suggested by the physicist E T Jaynes: "Probability as Logic". Learning and maximum entropy principle translate incompleteness into uncertainty. Bayesian inference offers a formal framework for reasoning with this uncertainty. The main contribution of this paper is the definition of a generic system of robotic programming and its experimental application. We illustrate it by programming a surveillance task with a mobile robot: the Khepera. In order to do this, we use generic programming resources called "descriptions". We show how to define and use these resources in an incremental way (reactive behaviors, sensor fusion, situation recognition and sequences of behaviors) within a systematic and unified framework.