Core Viewpoint - Current research on large language models (LLMs) is shifting from pre-training based on scaling laws to post-training focused on enhancing reasoning capabilities, particularly logical reasoning, which is crucial for addressing hallucination issues [1][4]. Group 1: Logical Reasoning Challenges - LLMs exhibit significant deficiencies in logical reasoning, categorized into two main issues: logical question answering and logical consistency [4][9]. - In logical question answering, LLMs struggle to generate correct answers when required to perform complex reasoning based on given premises and constraints [6][10]. - Logical consistency issues arise when LLMs provide contradictory answers to different questions, undermining their reliability in high-stakes applications [11][20]. Group 2: Research Methodologies - The review categorizes existing methods for enhancing logical reasoning into three main approaches: external solvers, prompt engineering, and pre-training with fine-tuning [15][18]. - External solver methods involve translating natural language logic problems into symbolic language expressions for resolution by external solvers [16]. - Prompt engineering focuses on designing prompts that guide LLMs to construct logical reasoning chains explicitly [17]. - Pre-training and fine-tuning methods aim to incorporate high-quality logical reasoning examples into the training datasets to improve model performance [18]. Group 3: Logical Consistency Types - Various forms of logical consistency are identified, including negation consistency, implication consistency, transitivity consistency, fact consistency, and compositional consistency [22][24][26][28]. - Each type of consistency has specific requirements, such as ensuring that contradictory statements cannot both be true (negation consistency) or that logical implications are maintained (implication consistency) [22][24]. - The review emphasizes the importance of developing methods to enhance logical consistency across multiple dimensions to improve LLM reliability [28][31]. Group 4: Future Research Directions - Future research should explore extending LLMs' reasoning capabilities to modal logic to handle uncertainty and developing efficient algorithms that satisfy multiple forms of logical consistency [30][31]. - There is a need for training LLMs in higher-order logic to address more complex reasoning challenges [31]. Conclusion - The comprehensive survey outlines the current state of research on LLMs' logical reasoning capabilities, highlighting significant challenges and proposing future research directions to enhance their performance in logical question answering and consistency [32].