The compositional rule of inference (CRI) proposed by Zadeh has been widely applied in artificial intelligence, control, data mining, image processing, decision making and so on. Recently, Li and Zeng [Li, D., Zeng, Q. Approximate reasoning with aggregation functions satisfying GMP rules, Artificial Intelligence Review (2022), https://doi.org/10.1007/s10462-022-10136-1] shown an A-compositional rule of inference (ACRI) method in which generalizes the t-norm to any aggregation function in CRI method and studied its validity using GMP rules. In this paper, we continue to investigate the validity of ACRI method from a logical view and an interpolative view. Specifically, to discuss the modus ponens (MP) and modus tollens (MT) properties of ACRI method based on well-known fuzzy implications with aggregation functions.

翻译：Zadeh提出的构成推论规则(CRI)已广泛应用于人工智能、控制、数据挖掘、图像处理、决策等。最近,Li和Zeng[Li,D.,Zeng,Q.Appiral 推理,其汇总功能符合GMP规则,人工智能审查(2022年),https://doi.org/10.1007/s10462-02-022-10136-1]显示A组合推论规则(ACRI)方法,其中将t-norm概括到CRI方法中的任何统合功能,并使用GMP规则研究其有效性。在本文件中,我们继续从逻辑观点和相互交织的观点研究ARI方法的有效性,具体来说,根据众所周知的模糊影响和总合功能,讨论ARI方法的手法(MP)和手法(MT)特性。