# Towards Unifying Logical Entailment and Statistical Estimation

arXiv: https://arxiv.org/abs/2202.13406 · HTML: https://mlsanity.com/paper/2202.13406/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 0 of its 13 references that are in the map.
- First posted on arXiv 27 Feb 2022.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Abstract (arXiv)

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.