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Towards Logically Consistent Language Models via Probabilistic Reasoning

Diego Calanzone, Stefano Teso, Antonio Vergari

TL;DR

The paper addresses the persistent challenges of factuality and self-consistency in large language models by proposing LoCo-LMs, which integrate principled probabilistic reasoning via a semantic loss over a knowledge base of facts and rules. By treating the model as a pool of truth beliefs and constraining it with ground facts and logical implications, the approach enforces consistency without relying on external reasoning tools. Empirical results on BeliefBank show that LoCo-LMs yield higher factuality and logical self-consistency than baselines, especially in low-data regimes, and can extrapolate to unseen facts with limited supervision. The work highlights the potential of neuro-symbolic, constraint-driven training to produce more reliable and scalable reasoning in LLMs, and points to future directions in expanding logical operators and cross-entity transfer of logical structure.

Abstract

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.

Towards Logically Consistent Language Models via Probabilistic Reasoning

TL;DR

The paper addresses the persistent challenges of factuality and self-consistency in large language models by proposing LoCo-LMs, which integrate principled probabilistic reasoning via a semantic loss over a knowledge base of facts and rules. By treating the model as a pool of truth beliefs and constraining it with ground facts and logical implications, the approach enforces consistency without relying on external reasoning tools. Empirical results on BeliefBank show that LoCo-LMs yield higher factuality and logical self-consistency than baselines, especially in low-data regimes, and can extrapolate to unseen facts with limited supervision. The work highlights the potential of neuro-symbolic, constraint-driven training to produce more reliable and scalable reasoning in LLMs, and points to future directions in expanding logical operators and cross-entity transfer of logical structure.

Abstract

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.
Paper Structure (10 sections, 6 equations, 2 figures, 3 tables)

This paper contains 10 sections, 6 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Tackling Factual & Consistent Inference with LoCo-LMs
  3. Setting.
  4. Experiments
  5. Conclusion and Further Work
  6. Training details
  7. Evaluation details
  8. Evaluation on the training distribution
  9. Temporal efficiency Analysis
  10. Semantic overlap between train and test

Figures (2)

  • Figure 1: Our LoCo-LMs are trained by compiling implication constraints in a semantic loss and applying them to some atomic facts as antecedents. At test time, they can predict the missing consequents more consistently and factually than other baselines (\ref{['table_A']}).
  • Figure 2: Pairwise cosine similarities between entities in the training distribution (calibration, rows) and the test distribution (silver, columns).