In the Sanlun school of Chinese Madhyamaka, logic and reasoning play a crucial role in understanding and interpreting the teachings. The school emphasizes the importance of using rational analysis and logical reasoning to gain a deeper understanding of the nature of reality and the ultimate truth.

One of the key teachings of the Sanlun school is the concept of the Threefold Nature of Reality, which states that all phenomena have three aspects - the dependent nature, the emptiness nature, and the perfect nature. This concept is based on the Madhyamaka philosophy, which asserts that all things are empty of inherent existence and are dependent on causes and conditions. To understand this complex concept, the Sanlun school relies heavily on logical reasoning and analysis.

The school also places great emphasis on the use of logic and reasoning to refute the concept of inherent existence. According to the Sanlun school, the belief in inherent existence is the root cause of suffering and delusion. Therefore, they use logical arguments and reasoning to demonstrate the emptiness of all phenomena and the lack of inherent existence.

In addition, the Sanlun school also employs the method of reductio ad absurdum, or the method of indirect proof, to refute the views of other schools and establish their own teachings. This method involves examining the logical consequences of a particular view and showing that it leads to absurd or contradictory conclusions. By using this method, the school aims to establish the superiority of their teachings and the correctness of their reasoning.

Moreover, the Sanlun school also utilizes the teachings of Nagarjuna, the founder of the Madhyamaka philosophy, to support their use of logic and reasoning. Nagarjuna's famous text, the Mulamadhyamakakarika, is considered a masterpiece of logical reasoning and is highly revered in the Sanlun school. The school also draws upon the teachings of other prominent Madhyamaka philosophers, such as Chandrakirti and Shantideva, to further strengthen their use of logic and reasoning.

In conclusion, logic and reasoning play a vital role in the teachings of the Sanlun school. They provide a systematic and analytical approach to understanding the nature of reality and the ultimate truth. By using logical arguments and reasoning, the school aims to guide individuals towards a deeper understanding of the Buddhist teachings and ultimately, towards liberation from suffering.