Necessary Conclusions in Moods with only One Necessary Premise A problem in Aristotelian modal syllogism

There are many criticisms about Aristotelian modal syllogism. Some logicians tried to provide adequate formulation of his total system but they were not successful. Therefore some logicians decided to account for those parts of the system which had been more controversial. The most controversial of the system is the "two barbaras" problem. The problem is about Aristotle's claim that moods with necessary major premise and assertoric minor premise have necessary conclusion while moods with assertoric major premise and necessary minor premise do not have necessary conclusion. Some logicians accept this, some believe that both of them have necessary conclusion, and some believe that both of them have assertoric conclusion. Rescher defended Aristotle's idea rather successfully. Moreover he thereby showed the consistency of this account with other parts of Aristotle's logic