Negative conclusion from affirmative premises
Negative conclusion from affirmative premises is a syllogistic fallacy committed when a categorical syllogism has a negative conclusion yet both premises are affirmative. The inability of affirmative premises to reach a negative conclusion is usually cited as one of the basic rules of constructing a valid categorical syllogism. Statements in syllogisms can be identified as the following forms:

 a: All A is B. (affirmative)
 e: No A is B. (negative)
 i: Some A is B. (affirmative)
 o: Some A is not B. (negative)

The rule states that a syllogism in which both premises are of form a or i (affirmative) cannot reach a conclusion of form e or o (negative). Exactly one of the premises must be negative to construct a valid syllogism with a negative conclusion. (A syllogism with two negative premises commits the related fallacy of exclusive premises.) Example (invalid aae form):
Premise: All colonels are officers. Premise: All officers are soldiers. Conclusion: Therefore, no colonels are soldiers. The aao-4 form is perhaps more subtle as it follows many of the rules governing valid syllogisms, except it reaches a negative conclusion from affirmative premises. Invalid aao-4 form:
All A is B. All B is C.
Therefore, some C is not A. This is valid only if A is a proper subset of B and/or B is a proper subset of C.  However, this argument reaches a faulty conclusion if A, B, and C are equivalent. In the case that A = B = C, the conclusion of the following simple aaa-1 syllogism would contradict the aao-4 argument above:

All B is A. All C is B. Therefore, all C is A. See also
 Affirmative conclusion from a negative premise, in which a syllogism is invalid because an affirmative conclusion is reached from a negative premise
 Fallacy of exclusive premises, in which a syllogism is invalid because both premises are negative

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Syllogistic fallacies