 Gilbert’s definition appears to contain some redundancy, since presumably an agent would not perceive A unless A is the case. Gilbert is evidently trying to give a more explicit account of single agent knowledge than Lewis and Aumann give. For Gilbert, agent \(i\) knows that a proposition \(E\) is the case if, and only if, \(\omega \in E\), that is, \(E\) is true, and either \(i\) perceives that the state of affairs \(E\) describes obtains or \(i\) can infer \(E\) as a consequence of other propositions \(i\) knows, given sufficient inferential capacity.