  We define and study the notions of q-deductive systems, p-deductive systems,
deductive systems, maximal and strongly maximal q-deductive systems in
quantum-Wajsberg algebras. We also introduce the notion of congruences induced
by deductive systems of a quantum-Wajsberg algebra, and we show that there is a
relationship between congruences and deductive systems. Furthermore, we define
the quotient quantum-Wajsberg algebra with respect to a deductive system, and
prove that the quotient quantum-Wajsberg algebra is locally finite if and only
if the deductive system is strongly maximal. Finally, we define the weakly
linear and quasi-linear quantum-Wajsberg algebras, and give a characterization
of weakly linear quotient quantum-Wajsberg algebras.
