On the mathematical modeling of syllogistic structures

The propositions express only a claim, a judgment, a proposal or a declaration. They are linguistic units, which consist of a subject, a predicate, and a conjunction and they have a true or false logical value and proclaim a judgment. Conditional propositions are propositions in which the judiciary depends on a condition. These propositions are formed by combining two simple propositions with the conjunction "if". Syllogism is called the derivation of a provision from two premises through deductive reasoning. In this study, conditional propositions that their structures are syllogistic, are modelled with directional graphs. It is evolved out of proposition "p are q" by accepting that the values of all conditional propositions that used are true. Exemplarily; a list of complex propositions that generate with conditional link is modelled with theory of graph. This graph is calculated in such a way as to nodes express propositions and edges express conditional link between two propositions. In that graph, other propositions that every structures can reach and create theorems with algorithm DFS (Depth First Search) was argued. As a result, new inferences that cannot appeared in a complex indicated propositions list are analysed and new propositions that are true and emerge after examination are shown.