Arc Representation of Syllogism on Venn Diagram: A New Method

In this article, which is written in the field of Aristotle logic in general and absolute Syllogism in particular, the aim is to present a new method for representing predicative propositions by considering the negative terms on the developed Vann diagram. This method is capable of displaying and inferring all possible results from two premises in all forms with any combination of negative and positive terms. It is also able to infer all the equations of each predicative proposition. This method is easy and decidable and having high expressive power. Conventional diagrammatic methods are either incapable of representing syllogism with negative terms or, if able to work with negative terms, do not have the desired visual representation that is the main purpose of diagrammatic representations. This method uses three-value valuation of lines and surfaces on a vann diagram, and the representation of each proposition is done by drawing a two-part arc.