A New Algorithmic Decision for Categorical Syllogisms via Caroll's Diagrams
This work addresses logical reasoning challenges in formal logic, but it appears incremental as it builds on existing diagrammatic methods.
The paper tackles the problem of determining the validity of categorical syllogisms by introducing SLCD, a formal system based on Carroll diagrams, and presents an effective algorithm for this purpose, though no concrete performance numbers are provided.
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.