  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.
