A syllogism (henceforth categorical unless otherwise specified) consists of three parts: the major premise, the minor premise, and the conclusion. In Aristotle, each of the premises is in the form "Some/all A belong to B," where "Some/All A" is one term and "belong to B" is another, but more modern logicians allow some variation. Each of the premises has one term in common with the conclusion: in a major premise, this is the major term (i.e., the predicate) of the conclusion; in a minor premise, it is the minor term (the subject) of the conclusion

Types of syllogism
Although there are infinitely many possible syllogisms, there are only a finite number of logically distinct types. We shall classify and enumerate them below. Note that the syllogisms above share the same abstract form:
Major premise: All M are P.
Minor premise: All S are M.
Conclusion: All S are P.
The premises and conclusion of a syllogism can be any of four types, which are labelled by letters[1] as follows.

The letters standing for the types of proposition (A, E, I, O) have been used since the medieval Schools to form mnemonic names for the forms. The meaning of the letters is given by the table:

Determining the validity of a syllogism involves determining the distribution of each term in each statement, meaning whether all members of that term are accounted for.

In simple syllogistic patterns, the fallacies of invalid patterns are:

Undistributed middle - Neither of the premises accounts for all members of the middle term, which consequently fails to link the major and minor term.

Illicit treatment of the major term - The conclusion implicates all members of the major term (P - meaning the proposition is negative); however, the major premise does not account for them all (i e P is either an affirmative predicate or a particular subject there).

Illicit treatment of the minor term - Same as above, but for the minor term (S - meaning the proposition is universal) and minor premise (where S is either a particular subject or an affirmative predicate).

Exclusive premises - Both premises are negative, meaning no link is established between the major and minor terms.

Affirmative conclusion from a negative premise - If either premise is negative, the conclusion must also be.

Existential fallacy - This is a more controversial one. If both premises are universal, i.e. "All" or "No" statements, one school of thought says they do not imply the existence of any members of the terms. In this case, the conclusion cannot be existential; i.e. beginning with "Some". Another school of thought says that affirmative statements (universal or particular) do imply the subject's existence, but negatives do not. A third school of thought says that the any type of proposition may or may not involve the subject's existence, and although this may condition the conclusion it does not affect the form of the syllogism.