Appeal to ignorance has a very specific structure: one argues that since there is no evidence _against_ a claim (including negative claims - i.e., that something is not the case) - that claim must be true. But this is at best, to point to a necessary condition - not a sufficient condition - for the truth of the claim.
1. P1: The health department could not prove that the committee was responsible for the outbreak of salmonella poisoning at the Apple Festival.
C1: Therefore, the committee is not responsible for the outbreak of salmonella poisoning at the Apple Festival.
2. Colonel North's convictions were thrown out Sept. 16 because special prosecutor Lawrence Walsh could not prove the the convictions were not influenced by the 1987 testimony North gave to Congress while under immunity from prosecution. ("North Case Dismissal Seen Aiding Chances of Gates Nomination," Christian Science Monitor, Wednesday, September 18, 1991, p. 9)
3. P1: The drug deprenyl is an effective anti-depressant, says Dr. J. John Mann, professor of psychiatry at the University of Pittsburgh.
P2: Dr. Mann asked these depressed patients if they had noticed any improvement in sexual desire, and several of them said they had.
P3: Deprenyl affects a certain neurotransmitter in the brain called dopamine.
[P4 : Dopamine affects sexual function.
C: The drug deprenyl is an aphrodisiac.
"they don't state whether there was another cause to increase sexual function, so it must have been the drug."
4. The government is hiding the remains of several UFO crashes, including alien bodies, in "Area 51," a top secret area of an Air Force base in the Southwest.
While the government has denied this claim, they've never proven that it was false. So I'm entitled to continue to believe that it is true.