Using Venn Diagrams to Perform Logic Reasoning: An Algorithm for Automating the Syllogistic Reasoning of Categorical Statements

I describe a Venn diagramming technique used to perform syllogistic reasoning on categorical statements. The notation uses overlapping circles to represent relationships among two or three sets, shadings to represent emptiness, and x sequences to represent nonemptiness. These notations allow one to easily visualize logic problems. I then discuss rules of manipulation that can be used to transform one Venn diagram into another valid Venn diagram. These rules provide us with a formal procedure for performing syllogistic reasoning—that is to say, they provide us with an algorithm for proving or disproving the validity of a syllogism. I extend the Venn diagramming algorithm for syllogistic reasoning to allow for more than three sets of information at a time. This technique makes use of tables, which is also very intuitive and highly visual. The tabular technique described is capable of processing a much larger variety of logic statements.