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

TL;DR

This work tackles the inefficiencies and unreliability of forward reasoning in natural language logical tasks by introducing Hypothesis-driven Backward Logical Reasoning (HBLR). HBLR uses confidence-aware symbolic translation to convert only high-confidence text into logic and then performs backward reasoning from the conclusion, aided by a verification mechanism. The approach achieves superior accuracy and efficiency across five benchmarks and demonstrates robustness to reasoning depth and model strength. By combining selective symbolic rigor with backward chaining, HBLR reduces translation errors, redundancy, and semantic drift, offering a practical path to more reliable LLM-based reasoning.

Abstract

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.

Figures (6)

• Figure 1: Conceptual comparison of reasoning paradigms. HBLR adopts a hypothesis-driven backward reasoning strategy with selective symbolic translation, enhancing precision and effectiveness.
• Figure 2: (a) Translation Error Rate Among SymbCoT Failure Cases in FOLIO and AR-LSAT (b) Ratio of essential tokens retained after pruning redundant steps from GPT-4-generated reasoning plans.
• Figure 3: Overview of the Hypothesis-driven Backward Logical Reasoning (HBLR) framework. Structural Filter and Semantic Verifier below illustrate the internal mechanisms of the Confidence-aware Symbolic Translation module.
• Figure 4: Comparison of selective translation (HBLR) with its two module variants: All-NL and All-FOL. HBLR consistently achieves higher accuracy across all datasets by balancing natural language and formal logic.
• Figure 5: Proportion of natural language retained by the Translation module across datasets. Retention varies by task, reflecting differences in translation confidence.