  In this paper a conditional logic is defined and studied. This conditional
logic, DmBL, is constructed as a deterministic counterpart to the Bayesian
conditional. The logic is unrestricted, so that any logical operations are
allowed. A notion of logical independence is also defined within the logic
itself. This logic is shown to be non-trivial and is not reduced to classical
propositions. A model is constructed for the logic. Completeness results are
proved. It is shown that any unconditioned probability can be extended to the
whole logic DmBL. The Bayesian conditional is then recovered from the
probabilistic DmBL. At last, it is shown why DmBL is compliant with Lewis'
triviality.
