 The extensive form of a dialogical game \(\mathcal{D}(\varphi)\) for \(\varphi\) is simply the tree representation of the game, where each path represents a play and branches represent terminal plays. Thus, the extensive form \(\mathfrak{E}_{\varphi}\) of \(\mathcal{D}(\varphi)\) is the tree (\(T\), \(\ell\), \(S\)) such that: