  Often in Software Engineering, a modeling formalism has to support scenarios
of inconsistency in which several requirements either reinforce or contradict
each other. Paraconsistent transition systems are proposed in this paper as one
such formalism: states evolve through two accessibility relations capturing
weighted evidence of a transition or its absence, respectively. Their weights
come from a specific residuated lattice. A category of these systems, and the
corresponding algebra, is defined as providing a formal setting to model
different application scenarios. One of them, dealing with the effect of
quantum decoherence in quantum programs, is used for illustration purposes.
