# Towards Logically Consistent Language Models via Probabilistic Reasoning

arXiv: https://arxiv.org/abs/2404.12843 · HTML: https://mlsanity.com/paper/2404.12843/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 0 of its 23 references that are in the map.
- First posted on arXiv 19 Apr 2024.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Built on by (most cited first, 2 of 2)

- [What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?](https://mlsanity.com/paper/2409.07953/) (2024)
- [Towards Annotation-Free Validation of MLLMs: A Vision-Language Logical Consistency Metric](https://mlsanity.com/paper/2605.06201/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are a promising venue for natural language understanding and generation tasks. However, current LLMs are far from reliable: they are prone to generate non-factual information and, more crucially, to contradict themselves when prompted to reason about beliefs of the world. These problems are currently addressed with large scale fine-tuning or by delegating consistent reasoning to external tools. In this work, we strive for a middle ground and introduce a training objective based on principled probabilistic reasoning that teaches a LLM to be consistent with external knowledge in the form of a set of facts and rules. Fine-tuning with our loss on a limited set of facts enables our LLMs to be more logically consistent than previous baselines and allows them to extrapolate to unseen but semantically similar factual knowledge more systematically.