Prompt-based methods have gained increasing attention on NLP and shown
validity on many downstream tasks. Many works have focused on mining these
methods' potential for knowledge extraction, but few explore their ability to
make logical reasoning. In this work, we focus on the effectiveness of the
prompt-based methods on first-order logical reasoning and find that the
bottleneck lies in logical negation. Based on our analysis, logical negation
tends to result in spurious correlations to negative answers, while
propositions without logical negation correlate to positive answers. To solve
the problem, we propose a simple but effective method, Negation Augmenting and
Negation Debiasing (NAND), which introduces negative propositions to
prompt-based methods without updating parameters. Specifically, these negative
propositions can counteract spurious correlations by providing "not" for all
instances so that models cannot make decisions only by whether expressions
contain a logical negation. Experiments on three datasets show that NAND not
only solves the problem of calibrating logical negation but also significantly
enhances prompt-based methods of logical reasoning without model retraining.

基于提示的方法在自然语言处理领域越来越受关注，并在许多下游任务中显示出其有效性。然而，鲜有研究探索这些方法在逻辑推理方面的能力。本研究针对提示方法在一阶逻辑推理方面的有效性进行研究，发现其中的瓶颈问题在于逻辑否定。根据我们的分析，逻辑否定往往导致与负回答的虚假相关性，而没有逻辑否定的命题则与正回答相关。为了解决这个问题，我们提出了一种简单而有效的方法，即 Negation Augmenting and Negation Debiasing（NAND），该方法引入了负命题到基于提示的方法中，而无需更新参数。具体而言，这些负命题通过为所有实例提供 “不” 来抵消虚假相关性，使模型不能仅通过表达式中是否包含逻辑否定来做决策。在三个数据集上的实验证明，NAND 不仅解决了逻辑否定校准的问题，还显著增强了基于提示方法在逻辑推理方面的性能，而无需重新训练模型。