# From Hypothesis to Premises: LLM-based Backward Logical Reasoning with Selective Symbolic Translation

arXiv: https://arxiv.org/abs/2512.03360 · HTML: https://mlsanity.com/paper/2512.03360/

## 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 25 of its 48 references that are in the map.
- First posted on arXiv 3 Dec 2025.

## Placed in

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

## Builds on (most cited first, 25 of 25)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [Faithful Logical Reasoning via Symbolic Chain-of-Thought](https://mlsanity.com/paper/2405.18357/) (2024)
- [Cumulative Reasoning with Large Language Models](https://mlsanity.com/paper/2308.04371/) (2023)
- [Beyond Accuracy: Evaluating the Reasoning Behavior of Large Language Models -- A Survey](https://mlsanity.com/paper/2404.01869/) (2024)
- [A Survey of Reasoning with Foundation Models](https://mlsanity.com/paper/2312.11562/) (2023)
- [Demystifying Chains, Trees, and Graphs of Thoughts](https://mlsanity.com/paper/2401.14295/) (2024)
- [AR-LSAT: Investigating Analytical Reasoning of Text](https://mlsanity.com/paper/2104.06598/) (2021)
- [Bidirectional Language Models Are Also Few-shot Learners](https://mlsanity.com/paper/2209.14500/) (2022)
- [How Likely Do LLMs with CoT Mimic Human Reasoning?](https://mlsanity.com/paper/2402.16048/) (2024)
- [Time Series Forecasting via Reasoning: A Slow-Thinking Approach with Reinforcement Fine-Tuned LLMs](https://mlsanity.com/paper/2506.10630/) (2025)
- [Formal Specifications from Natural Language](https://mlsanity.com/paper/2206.01962/) (2022)
- [LogicAsker: Evaluating and Improving the Logical Reasoning Ability of Large Language Models](https://mlsanity.com/paper/2401.00757/) (2024)
- [Can Slow-thinking LLMs Reason Over Time? Empirical Studies in Time Series Forecasting](https://mlsanity.com/paper/2505.24511/) (2025)
- [TableMind: An Autonomous Programmatic Agent for Tool-Augmented Table Reasoning](https://mlsanity.com/paper/2509.06278/) (2025)
- [An Examination on the Effectiveness of Divide-and-Conquer Prompting in Large Language Models](https://mlsanity.com/paper/2402.05359/) (2024)
- [SymBa: Symbolic Backward Chaining for Structured Natural Language Reasoning](https://mlsanity.com/paper/2402.12806/) (2024)
- [Are LLMs Stable Formal Logic Translators in Logical Reasoning Across Linguistically Diversified Texts?](https://mlsanity.com/paper/2506.04575/) (2025)

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

- [Wiring the 'Why': A Unified Taxonomy and Survey of Abductive Reasoning in LLMs](https://mlsanity.com/paper/2604.08016/) (2026)
- [CEDAR-GRPO: Process-Aware Reinforcement Learning for General Abductive Reasoning in LLMs](https://mlsanity.com/paper/2608.14791/) (2026)

## Abstract (arXiv)

Logical reasoning is a core challenge in natural language understanding and a fundamental capability of artificial intelligence, underpinning scientific discovery, mathematical theorem proving, and complex decision-making. Despite the remarkable progress of large language models (LLMs), most current approaches still rely on forward reasoning paradigms, generating step-by-step rationales from premises to conclusions. However, such methods often suffer from redundant inference paths, hallucinated steps, and semantic drift, resulting in inefficient and unreliable reasoning. In this paper, we propose a novel framework, Hypothesis-driven Backward Logical Reasoning (HBLR). The core idea is to integrate confidence-aware symbolic translation with hypothesis-driven backward reasoning. In the translation phase, only high-confidence spans are converted into logical form, such as First-Order Logic (FOL), while uncertain content remains in natural language. A translation reflection module further ensures semantic fidelity by evaluating symbolic outputs and reverting lossy ones back to text when necessary. In the reasoning phase, HBLR simulates human deductive thinking by assuming the conclusion is true and recursively verifying its premises. A reasoning reflection module further identifies and corrects flawed inference steps, enhancing logical coherence. Extensive experiments on five reasoning benchmarks demonstrate that HBLR consistently outperforms strong baselines in both accuracy and efficiency.