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Jack comments on Logical Uncertainty as Probability - Less Wrong
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So then it isn't true that P(S|X) = 1 if and only if S∈OLC(X).
If X = { "2*2=4" }, then P("2*2=4 ∨ 0=1" | X) = 1, because "2*2=4 ∨ 0=1" ∈ OLC(X).
However, P("2*3=6" | X) < 1, although P("2*3=6" | X ∪ {"2*3=6"}) = 1.