Whether the focus lies on Bayes' rule or on Bayes' theorem, the common theme in the above-mentioned arguments is that they approach Bayesian statistical inference from a logical angle, and focus on its internal coherence or consistency (cf. Howson 2003). While its use in statistics is undeniably inductive, Bayesian inference thereby obtains a deductive, or at least non-ampliative character: everything that is concluded in the inference is somehow already present in the premises. In Bayesian statistical inference, those premises are given by the prior over the hypotheses, \(P(h_{\theta})\) for \(\theta \in \Theta\), and the likelihood functions, \(P(s \mid h_{\theta})\), as determined for each hypothesis \(h_{\theta}\) separately.  These premises fix a single probability assignment over the space \(M \times S\) at the outset of the inference. The conclusions, in turn, are straightforward consequences of this probability assignment. They can be derived by applying theorems of probability theory, most notably Bayes' theorem. Bayesian statistical inference thus becomes an instance of probabilistic logic (cf. Hailperin 1986, Halpern 2003, Haenni et al 2011).