In this paper, we deal with a calculus system SLCD (Syllogistic Logic with Carroll Diagrams), which gives a formal approach to logical reasoning with diagrams, for representations of the fundamental Aristotelian categorical propositions and show that they are closed under the syllogistic criterion of inference which is the deletion of middle term. Therefore, it is implemented to let the formalism comprise synchronically bilateral and trilateral diagrammatical appearance and a naive algorithmic nature. And also, there is no need specific knowledge or exclusive ability to understand as well as to use it. Consequently, we give an effective algorithm used to determine whether a syllogistic reasoning valid or not by using SLCD.

翻译：在本文中,我们处理的是微积分系统SLCD(用卡罗尔图表的逻辑逻辑学),它为图表的逻辑推理提供了一种正式的方法,用以表述亚里士多德派的绝对基本主张,并表明这些主张是依据中期内删除的推论的逻辑标准封闭的。因此,它的实施是为了让形式主义包括同步的双边和三边图表外观和天真的算法性质。此外,也没有必要具体的知识或独家能力来理解和使用它。因此,我们给出了一种有效的算法,用来确定一种逻辑推理是否有效,用SLCD来确定是否有效。