Conventionally, valid deductive arguments with two premises and one conclusion are called syllogisms in classical logic. These arguments are among the most discussed and studied logical forms since Aristotle. Specifically, a categorical syllogism is an argument consisting of exactly three categorical propositions (two premises and one conclusion) containing exactly three categorical terms, each of which is used exactly twice.
One of the terms is used as the subject term of the conclusion of the syllogism. It is called the minor term of the syllogism . The major term of the syllogism is a term that is used as the predicate term of its conclusion. The third term in the syllogism does not occur in the conclusion, but must be used in each of its premises. It is called the middle term. An example is an argument such as:
all men are animals (first premise)
all animals are mortal (second premise)all men are mortal (conclusion)
where ``man'' is the minor term, ``are-mortal'' is the major term, and ``animals'' is the middle term.