 Examples of PAL-friendly theories include the common “logic of belief” (multi-modal \(\mathsf{KD45}\)), the common “logic of knowledge” (multi-modal \(\mathsf{S5}\)), multi-modal \(\mathsf{K}\), multi-modal \(\mathsf{T}\), multi-modal \(\mathsf{S4}\), and certain logics that mix modal operators of the previously mentioned types (e.g., \(\mathsf{S5}\) for \([a]\) and \(\mathsf{T}\) for all other agent modal operators \([b]\)). Fixing a PAL-friendly theory \(\L\), we easily obtain an axiomatic theory of public announcement logic based on \(\L\) as follows. 