 2D matrices can be used to represent this sort of partial semantic understanding. O’Leary knows that \(if\) the man in front of him is the author of the famous article, then ‘Lloyd = I.L. Humberstone’ expresses a necessary truth; and he knows that \(if\) the man in front of him isn’t the author, the sentence expresses a necessary falsehood. What O’Leary doesn’t know is which of these two possibilities corresponds to his actual situation. Call the first possibility i and the second j. O’Leary’s epistemic situation can then be summed up in a 2D matrix: