  Logical propositions with the fuzzy modality "Probably" are shown to obey an
uncertainty principle very similar to that of Quantum Optics. In the case of
such propositions, the partial truth values are in fact probabilities. The
corresponding assertions in the metalanguage, have complex assertion degrees
which can be interpreted as probability amplitudes. In the logical case, the
uncertainty relation is about the assertion degree, which plays the role of the
phase, and the total number of atomic propositions, which plays the role of the
number of modes. In analogy with coherent states in quantum physics, we define
"quantum coherent propositions" those which minimize the above logical
uncertainty relation. Finally, we show that there is only one kind of compound
quantum-coherent propositions: the "cat state" propositions.
