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

2025-12-03

AI Summary

Current large language models (LLMs) rely on forward-stepwise reasoning, suffering from path redundancy, hallucinated intermediate steps, and semantic drift—leading to low logical reasoning efficiency and poor reliability. To address this, we propose Hypothesis-Driven Backward Logical Reasoning (HBLR), a novel framework that initiates inference from the conclusion and proceeds backward. HBLR first employs a confidence-aware symbolic translation mechanism to selectively convert natural language premises into first-order logic representations. It then performs backward deduction while incorporating a dual-reflection module—comprising translation reflection (ensuring semantic fidelity) and reasoning reflection (guaranteeing logical consistency)—to jointly model natural language and formal logic. Evaluated on five logical reasoning benchmarks, HBLR significantly outperforms strong baselines, achieving state-of-the-art accuracy and minimal inference steps. These results empirically validate the effectiveness of hypothesis-driven backward reasoning in enhancing both the robustness and efficiency of LLM-based logical inference.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Natural Language Processing: (Large) Language Models

Application Category

• Search and Retrieval-Augmented AI: Large language models for search
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• Improves logical reasoning accuracy by backward verification
• Reduces redundant steps and hallucinations in inference
• Enhances efficiency with selective symbolic translation

Innovation

• Backward reasoning from hypothesis to premises
• Selective symbolic translation of high-confidence spans
• Reflection modules for semantic fidelity and logical coherence