Affirmative conclusion from a negative premise

An affirmative conclusion from a negative premise (also illicit negative) occurs when a categorical syllogism has a positive conclusion, but one or two negative premises.

It is a syllogistical fallacy and a formal fallacy.

Forms
An affirmative conclusion from a negative premise can take three forms:

First form: (single "not", second premise)

Second form: (single "not", first premise)

Third form (called "exclusive premises"): (double "not")

Legitimate use
It is acceptable to have an affirmative premise and a negative premise as long as the conclusion is negative. The only problem is when the conclusion is positive. Two examples make this clear:

Negative conclusion:

Positive conclusion:

Problem
The fallacy is invalid because any valid categorical syllogism with one (or more) negative premise(s) must have a negative conclusion.

Examples

 * The exclusion of 'humans' from the 'birds' category gives no reason to include humans in the 'reptile' category. It is easily proven false by finding an example that disproves the conclusion, but doesn't invalidate the premises, such as finding a human that isn't a reptile.