 The principle \(\neg B_{a}\bot\) is, on Kripke models, equivalent with the principle D, \(B_{a}\varphi\rightarrow\widehat{B}_{a}\varphi\). Hence the validity of \(\neg B_{a}\bot\) requires serial frames. Witness, e.g., its failure in \(w_{1}\) above: As there are no worlds accessible through \(R_{B}\), all accessible worlds satisfy \(\bot\). Hence \(w_{1}\) satisfies \(B_{a}\bot\), violating consistency. Notice also that \(\neg B_{a}\bot\) may be re-written to \(\widehat{B}_{a}\top\), which is true at a world just in case some world is accessible through \(R_{B}\). Its validity thus ensures seriality.