Aspect-term sentiment analysis (ATSA) is an important task that aims to infer the sentiment towards the given aspect-terms. It is often required in the industry that ATSA should be performed with interpretability, computational efficiency and high accuracy. However, such an ATSA method has not yet been developed. This study aims to develop an ATSA method that fulfills all these requirements. To achieve the goal, we propose a novel Sentiment Interpretable Logic Tensor Network (SILTN). SILTN is interpretable because it is a neurosymbolic formalism and a computational model that supports learning and reasoning about data with a differentiable first-order logic language (FOL). To realize SILTN with high inferring accuracy, we propose a novel learning strategy called the two-stage syntax knowledge distillation (TSynKD). Using widely used datasets, we experimentally demonstrate that the proposed TSynKD is effective for improving the accuracy of SILTN, and the SILTN has both high interpretability and computational efficiency.