Bayes Meets Entailment and Prediction: Commonsense Reasoning with Non-monotonicity, Paraconsistency and Predictive Accuracy
This work addresses the foundational problem of unifying logical reasoning and machine learning under a Bayesian framework, offering a new approach to handle inconsistent knowledge and improve predictive accuracy for AI systems.
This paper proposes a generative model for logical consequence relations, framing the truth value of a sentence as probabilistically generated from world states. This model is shown to characterize classical, paraconsistent, and nonmonotonic consequence relations, and it introduces a new relation that improves reasoning with inconsistent knowledge. Additionally, the generative model yields a new classification algorithm that surpasses several existing algorithms in predictive accuracy and complexity on the Kaggle Titanic dataset.
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.