  Coherent spaces spanned by a finite number of coherent states, are
introduced. Their coherence properties are studied, using the Dirac contour
representation. It is shown that the corresponding projectors resolve the
identity, and that they transform into projectors of the same type, under
displacement transformations, and also under time evolution. The set of these
spaces, with the logical OR and AND operations is a distributive lattice, and
with the logical XOR and AND operations is a Boolean ring (Stone\rq{}s
formalism). Applications of this Boolean ring into classical CNOT gates with
$n$-ary variables, and also quantum CNOT gates with coherent states, are
discussed.
