Bayes Meets Entailment and Prediction: Commonsense Reasoning with
  Non-monotonicity, Paraconsistency and Predictive Accuracy
  The recent success of Bayesian methods in neuroscience and artificial
intelligence gives rise to the hypothesis that the brain is a Bayesian machine.
Since logic and learning are both practices of the human brain, it leads to
another hypothesis that there is a Bayesian interpretation underlying both
logical reasoning and machine learning. In this paper, we introduce a
generative model of logical consequence relations. It formalises the process of
how the truth value of a sentence is probabilistically generated from the
probability distribution over states of the world. We show that the generative
model characterises a classical consequence relation, paraconsistent
consequence relation and nonmonotonic consequence relation. In particular, the
generative model gives a new consequence relation that outperforms them in
reasoning with inconsistent knowledge. We also show that the generative model
gives a new classification algorithm that outperforms several representative
algorithms in predictive accuracy and complexity on the Kaggle Titanic dataset.
