Affirmative conclusion from a negative premise (illicit negative) is a formal fallacy that is committed when a categorical syllogism has a positive conclusion and one or two negative premises.

For example:

The only thing that can be properly inferred from these premises is that some things that are not fish cannot fly, provided that dogs exist.

Or:

This could be illustrated mathematically as

It is a fallacy because any valid forms of categorical syllogism that assert a negative premise must have a negative conclusion.