The calculus of partial propositional functions has been introduced in [2]. It is a variant of the classical propositional calculus, a variant which takes into account that pairs of propositions may be "incompatible" and cannot therefore be connected. As is well known, such pairs are considered in Quantum Theory; but they may also be said to occur in natural languages. Difficulties arising from propositions of the type "If two times two are five, then there exist centaurs' seem to be due as much to incompatibility as to material implication.