  One operation, common to all justification logics, is  application, written like multiplication. The idea is, if  \(s\) is a justification for \(A \rightarrow B\) and  \(t\) is a justification for \(A\), then  [\(s\cdot t\)] is a justification for   \(B\)[1].  That is, the validity of the following is generally assumed: