Playing with or without a list of announcements?
In a previous presentation, I have argued that a public announcement does not correspond to any conditional connectives. But in fact there are algorithms of translation that turn any public announcement in a conditional way. These translations do not yield an immediate material implication of annoucement propositions. They give us complex or embedded conditionals whose complexity directly depends of the post-condition of the announcement operator. Now, our aim is to compare the dialogues with those propositions (the one with the public announcement operator on the one hand and its corresponding translation on the other hand). As we shall see, such a study underlines the meaning of the list of announcements. This list represents the story of the commitment of the players. It emphasizes the two distinct levels: play and strategy level which occur in the dialogical framework. The comparison between them also suggests some improvements of the rule (SR-A.1) that will probably entail a weakening of the formal rule.