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In this paper, we deal with a calculus system SLCD (Syllogistic Logic withCarroll Diagrams), which gives a formal approach to logical reasoning withdiagrams, for representations of the fundamental Aristotelian categoricalpropositions and show that they are closed under the syllogistic criterion ofinference which is the deletion of middle term. Therefore, it is implemented tolet the formalism comprise synchronically bilateral and trilateraldiagrammatical appearance and a naive algorithmic nature. And also, there is noneed specific knowledge or exclusive ability to understand as well as to useit. Consequently, we give an effective algorithm used to determine whether asyllogistic reasoning valid or not by using SLCD.

A New Algorithmic Decision for Categorical Syllogisms via Caroll's Diagrams