  We derive an analogue of the quantum total probability rule by constructing a
probability theory based on paraconsistent logic. Bayesian probability theory
is constructed upon classical logic and a desiderata, that is, a set of desired
properties that the theory must obey. We construct a new probability theory
following the desiderata of Bayesian probability theory but replacing the
classical logic by paraconsistent logic. This class of logic has been conceived
to handle eventual inconsistencies or contradictions among logical propositions
without leading to the trivialisation of the theory. Within this Paraconsistent
bayesian probability theory it is possible to deduce a new total probability
rule which depends on the probabilities assigned to the inconsistencies.
Certain assignments of values for these probabilities lead to expressions
identical to those of Quantum mechanics, in particular to the quantum total
probability rule obtained via symmetric informationally complete positive-
operator valued measure.
