Absence of evidence is not evidence of absence: Bayesian view? (2021)

"Absence of evidence is not evidence of absence" has been interpreted both probabilistically and deterministically. As suited to the question, the answers here assume the probabilistic form (PF).

  PF: If you look and fail to observe evidence for A, 
      that does not support lowering your estimated probability of A.

As the accepted answer says, "When the hypothesis being true or false changes the probability of the observation, evidence is contributed." So, PF is false, except in the case where P(observation|A) = 0.

However, popular use of the aphorism generally seems to assume the deterministic form (DF).

  DF: If you look and fail to observe evidence for A, 
      that does not imply not-A.

DF is a caution against the logical fallacy of argumentum ad ignorantiam, an argument of the form: There is no reason that A; therefore, not-A.

It turns out that DF is not always true. It is false when you are certain to observe evidence if A is true, that is, P(observation|A) = 1. In philosophy, this requirement is called epistemic coverage.

The major work on DF is Douglas Walton's Arguments from Ignorance (1996), where he covers the history of argumentum ad ignorantiam and practical examples of where DF is or is not true. Walton later worked on application to AI and the problem of reasoning with restricted information.