There is a difficult problem about the interpretation of Aristotle's logic from a viewpoint of modern logic, that is, a problem of the existential import. This problem may be stated thus: whether a proposition treated in Aristotle's logic contains the existence of something that is denoted by the subject of that proposition. The famous formalization of Aristotle's logic by J. Lukasiewicz does not shed the light on this problem. In this way, however, we cannot prove many Aristotelian theses within such system. And the difficulties converge to a problem, that is, how we may introduce the existential import of a proposition into the system. The syntactical solution offered by A.N. Prior, Strawson and others has a serious shortcoming, i.e., separation from the usual meaning of a statement of ordinary language. And this defect is fatal to the interpretation of Aristotle's logic, because Aristotle has aimed to elucidate the logic of ordinary speeches and discussions. the second way for avoiding the difficulties is offered by Strawson in the term of "presupposition" of a statement. According to his assertion, semantical solution by Strawson is called a "realistic" solution in contrast with a "formalistic" solution. But his solution may be restated from the standpoint of formalist, that is, we may restate his presupposition as one of the semantical rules of a formal system. But such a mechanical solution introduces serious difficulties to a system of predicate calculus. I have shown in this paper how such considerations bring a sort of "informal" element in a usual system of predicate calculus.