Suppose that an agent \(A_{1}\) reasons in a sound theory \(T_{1}\), and an agent \(A_{2}\) reasons in a theory \(T_{2}\), such that \(T_{1}\) proves that \(T_{2}\) is sound. Now suppose \(A_{1}\) is trying to reason in a way that is legible to \(A_{2}\), in the sense that \(A_{2}\) can rely on \(A_{1}\) to reach correct conclusions. One way of doing this is for \(A_{1}\) to restrict itself to some weaker theory \(T_{3}\), which \(T_{2}\) proves is sound, for the purposes of any reasoning that it wants to be legible to \(A_{2}\). Of course, in order for this to work, not only would \(A_{1}\) have to restrict itself to using \(T_{3}\), but \(A_{2}\) would to trust that \(A_{1}\) had done so. A plausible way for that to happen is for \(A_{1}\) to reach the decision quickly enough that \(A_{2}\) can simulate \(A_{1}\) making the decision to restrict itself to using \(T_{3}\). |