 If \(A\) is common (or \(m\)th level mutual) knowledge at world \(\omega\), then \(A\) is common \((m\)th level) \(p\)-belief at \(\omega\) for every value of \(p\). So mutual and common \(p\)-beliefs formally generalize the mutual and common knowledge concepts. However, note that \(\mathbf{B}^1_{N^*}(A)\) is not necessarily the same proposition as \(\mathbf{K}^{*}_N (A)\), that is, even if \(A\) is common 1-belief, \(A\) can fail to be common knowledge.