论文标题
要统一逻辑构成和统计估计
Towards Unifying Logical Entailment and Statistical Estimation
论文作者
论文摘要
本文为数据驱动的逻辑推理的形式逻辑解释提供了一种生成模型。关键思想是将解释表示为正式逻辑模型的可能性是真实的。使用可能性，贝叶斯定理给定公式给出了模型的后部。后验代表了对形式逻辑的反向解释，它寻求使公式为真的模型。在所有前提都是真实的模型中，可能性和后部导致贝叶斯学习的可能性是真实的。本文着眼于贝叶斯学习的统计和逻辑特性。结果表明，生成模型是逻辑和统计中几种不同类型推理的统一理论。
This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the likelihood, Bayes' theorem gives the posterior of the model being the case given the formula. The posterior represents an inverse interpretation of formal logic that seeks models making the formula true. The likelihood and posterior cause Bayesian learning that gives the probability of the conclusion being true in the models where all the premises are true. This paper looks at statistical and logical properties of the Bayesian learning. It is shown that the generative model is a unified theory of several different types of reasoning in logic and statistics.
