A Simple Decision Method for Syllogistic

Abstract

We present a method of digraphs for Syllogistic that uses only two rules for testing the validity of syllogisms without existential import and a third rule for cases in which the existential import of terms is used. This method derives from Martin Gardner’s network method for Classical Propositional Logic, preserving the iconicity features that Gardner attributes to the propositional case also in the case of Syllogistic. We will first present the graphical representations and the rules for manipulating these representations in the case of syllogisms in which the existential import of terms are not admitted. Then, we will extend the method with a graphical representation for the existential import and with a new rule for the manipulation of this representation. Finally, we will show some applications of the method. It was first presented in Portuguese in Cognitio 14(2013): 221–234.