<p>Inspired by the operational quantum logic program, we have the contention that probabilities can be viewed as a derived concept, even in a reconstruction program of quantum mechanics. In a series of paper, the author has proposed an operational description of physical theories based on a possibilistic semantic (in a sense, the ‘probabilities’ are replaced by statements associated to a semantic domain made of three values ‘indeterminate’, ‘definitely YES’, ‘definitely NO’). After a careful analysis of the notions of incompatibility between measurements, the present paper intents to develop one step further our operational formalism. We show the existence of entangled states and exploit this result to show the existence of the steering of some states by a pair of incompatible measurements. Then, we show the existence of states which are Bell non-local with respect to two pairs of incompatible measurements.</p>