Probing the Symbolic Logical Reasoning Ability of Large Language Models

Large Language Models (LLMs) have achieved significant successes in various research domains by learning the relationship between words. However, while these models are capable of making predictions and inferences based on the learned patterns, they lack logical reasoning abilities, which are crucial for solving problems in both theoretical and practical domains. In addition, traditional logic inference methods are effective in solving problems that are based on logic, but not suitable for general tasks such as recommendations. In response to these challenges, this paper introduces a Logical Large Language Model (L3M) that integrates the strengths of logical reasoning and large language models. The data in L3M is represented in logical expressions and the model uses logical constraints to learn the rules of basic logical operations such as And, Or, and Not. We conduct experiments on both theoretical tasks (solving logical equations) and practical tasks (recommender systems). The results of our theoretical experiments demonstrate that L3M is highly effective in solving logical expressions and variables. Additionally, L3M outperforms the state-of-the-art recommendation models in sequential recommendation tasks.