 A hypothesis \(H\) is  verirefutable  if it is equivalent to the conjunction of a verifiable and a refutable hypothesis (given background knowledge): \(H = (V\) and \(R)\) where \(V\) is verifiable and R is refutable. For example, the hypothesis “exactly 2 swans are black” is verirefutable, since it is equivalent to the conjunction of the verifiable hypothesis “at least 2 swans are white” and the refutable hypothesis “at most 2 swans are white”. The term “verirefutable” is due to [Genin and Kelly 2015]; it signifies that when a verirefutable hypothesis is true, there is some initial condition after which the hypothesis is refutable, that is, the hypothesis will be falsified by data if it is false. Baltag et al. refer to verirefutable hypotheses as locally closed. They establish the following characterization theorem for reliable learning [Baltag et al. 2015].