# Improving Symbolic Translation of Language Models for Logical Reasoning

arXiv: https://arxiv.org/abs/2601.09446 · HTML: https://mlsanity.com/paper/2601.09446/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 9 of its 38 references that are in the map.
- First posted on arXiv 14 Jan 2026.

## Placed in

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

## Builds on (most cited first, 9 of 9)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Phi-4-Mini Technical Report: Compact yet Powerful Multimodal Language Models via Mixture-of-LoRAs](https://mlsanity.com/paper/2503.01743/) (2025)
- [A Survey on Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2402.13116/) (2024)
- [Formal Mathematical Reasoning: A New Frontier in AI](https://mlsanity.com/paper/2412.16075/) (2024)
- [Logical Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2502.09100/) (2025)
- [Large Language Models Meet Symbolic Provers for Logical Reasoning Evaluation](https://mlsanity.com/paper/2502.06563/) (2025)
- [JustLogic: A Comprehensive Benchmark for Evaluating Deductive Reasoning in Large Language Models](https://mlsanity.com/paper/2501.14851/) (2025)

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

- [Instruct, Not Answer: Using Instruction Privileges in On-Policy Context Distillation](https://mlsanity.com/paper/2609.32201/) (2026)
- [Quizzing the Translation: A Prover-Grounded Evaluation Metric for NLrightarrowFOL](https://mlsanity.com/paper/2609.33612/) (2026)

## Abstract (arXiv)

The use of formal language for deductive logical reasoning aligns well with language models (LMs), where translating natural language (NL) into first-order logic (FOL) and employing an external solver results in a verifiable and therefore reliable reasoning system. However, smaller LMs often struggle with this translation task, frequently producing incorrect symbolic outputs due to formatting and translation errors. Existing approaches typically rely on self-iteration to correct these errors, but such methods depend heavily on the capabilities of the underlying model. To address this, we first categorize common errors and fine-tune smaller LMs using data synthesized by large language models. The evaluation is performed using the defined error categories. We introduce incremental inference, which divides inference into two stages, predicate generation and FOL translation, providing greater control over model behavior and enhancing generation quality as measured by predicate metrics. This decomposition framework also enables the use of a verification module that targets predicate-arity errors to further improve performance. Our study evaluates three families of models across four logical-reasoning datasets. The comprehensive fine-tuning, incremental inference, and verification modules reduce error rates, increase predicate coverage, and improve reasoning performance for smaller LMs, moving us closer to developing reliable and accessible symbolic-reasoning systems.