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

TL;DR

This paper introduces a Bayesian generative model of logical consequence that unifies classical, paraconsistent, and nonmonotonic reasoning, and demonstrates its effectiveness in reasoning with inconsistent knowledge and in classification tasks.

Contribution

It presents a novel Bayesian generative model that formalizes logical consequence relations and improves reasoning with inconsistency and predictive accuracy.

Findings

Outperforms existing reasoning methods with inconsistent knowledge.

Achieves higher predictive accuracy on Kaggle Titanic dataset.

Unifies classical, paraconsistent, and nonmonotonic logic under a Bayesian framework.

Abstract

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.