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This paper gives a generative model of the interpretation of formal logic fordata-driven logical reasoning. The key idea is to represent the interpretationas likelihood of a formula being true given a model of formal logic. Using thelikelihood, Bayes' theorem gives the posterior of the model being the casegiven the formula. The posterior represents an inverse interpretation of formallogic that seeks models making the formula true. The likelihood and posteriorcause Bayesian learning that gives the probability of the conclusion being truein the models where all the premises are true. This paper looks at statisticaland logical properties of the Bayesian learning. It is shown that thegenerative model is a unified theory of several different types of reasoning inlogic and statistics.

Towards Unifying Logical Entailment and Statistical Estimation