What do you mean by special premise?

The special premise is existential proposition, which contains existential quantifiers. The form is "some s are p" or "some s are not p"

There are many rules in syllogism: for example, an event or small event is not GAI in the premise, so it is not Gai in the conclusion; Two negative premises cannot draw a conclusion; One of the premises is negative, and the conclusion should also be negative; The conclusion is negative, and one of the preconditions must be negative; Two special premises can't reach a conclusion; One of the premises is special, and the conclusion must be special.

In syllogism reasoning, it is impossible to deduce the full name conclusion from the special premise. Similarly, we can't deduce the full name proposition from the proper name proposition.

The concept of special name in syllogism

Traditional logic assumes that the main item (minor item) of the conclusion is not empty, that is, the elements of the set represented by this item exist. This assumption ensures the validity of the nine formulas after the semicolon in the above four grids, and the validity of the formula 15 before the semicolon is not affected by this assumption. As you can see, the nine valid expressions after the semicolon all have one characteristic, that is, the conclusion is special, provided that the full name is given.

According to Boolean's point of view, the full name proposition does not contain existence, that is, "proper name proposition cannot be deduced only from full name proposition" (generally speaking, proper name proposition is considered to have the meaning of existence, and "some A is B" means "there is an A, and that A is B"). For example, "all cars are vehicles" does not mean "cars exist", so he thinks that syllogism only has 15 valid expressions before semicolons.