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The recent success of Bayesian methods in neuroscience and artificialintelligence 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 toanother hypothesis that there is a Bayesian interpretation underlying bothlogical reasoning and machine learning. In this paper, we introduce agenerative model of logical consequence relations. It formalises the process ofhow the truth value of a sentence is probabilistically generated from theprobability distribution over states of the world. We show that the generativemodel characterises a classical consequence relation, paraconsistentconsequence relation and nonmonotonic consequence relation. In particular, thegenerative model gives a new consequence relation that outperforms them inreasoning with inconsistent knowledge. We also show that the generative modelgives a new classification algorithm that outperforms several representativealgorithms in predictive accuracy and complexity on the Kaggle Titanic dataset.

Bayes Meets Entailment and Prediction: Commonsense Reasoning with Non-monotonicity, Paraconsistency and Predictive Accuracy