Definition of a Deterministic Bayesian Logic

The Bayesian logic is generally associated to the definition of a prior probabilistic law. Conditional algebra have been investigated by some authors though, but somehow the background framework is still probabilistic and the entire logic is not specified. In this paper, the definition of a Deterministic Bayesian Logic is proposed. This logic is completely independent of any notion of probability. The coherence of this logic is proven and various logical theorems are derived. It is shown that this logic is probabilizable and avoids the negative result of Lewis. At last the probabilistic Bayesian rule is recovered by posteriorly probabilizing our logic.