A new algorithmic decision for categorical syllogisms via Carroll's diagrams.

In this paper, we propose a new effective algorithm for the categorical syllogisms by using a calculus system Syllogistic Logic with Carroll Diagrams, which determines a formal approach to logical reasoning with diagrams, for representations of the fundamental Aristotelian categorical syllogisms. We show that this logical reasoning is closed under the syllogistic criterion of inference. Therefore, the calculus system is implemented to let the formalism which comprises synchronically bilateral and trilateral diagrammatical appearance and naive algorithmic nature. And also, there is no need specific knowledge or exclusive ability to understand this decision procedure as well as to use it in an algorithmic system. Consequently, the empirical contributions of this paper are to design a polynomial-time algorithm at the first time in the literature to conduce to researchers getting into the act in different areas of science used categorical syllogisms such as artificial intelligence, engineering, computer science and etc. [ABSTRACT FROM AUTHOR]