  This paper gives a generative model of the interpretation of formal logic for
data-driven logical reasoning. The key idea is to represent the interpretation
as likelihood of a formula being true given a model of formal logic. Using the
likelihood, Bayes' theorem gives the posterior of the model being the case
given the formula. The posterior represents an inverse interpretation of formal
logic that seeks models making the formula true. The likelihood and posterior
cause Bayesian learning that gives the probability of the conclusion being true
in the models where all the premises are true. This paper looks at statistical
and logical properties of the Bayesian learning. It is shown that the
generative model is a unified theory of several different types of reasoning in
logic and statistics.
