 This integration of the “local” perspective of the players into the framework is an important proposal. Dialogical contexts are labels used to identify different parts (subplays) of a given dialogue and thus keep track of the information flow between these parts. This can be seen as a step towards hybridation (having syntactical tools to name states or worlds). Patrick Blackburn (2001) argued, however, that a thorough discussion of the benefits of such an integration advocates for a complete hybridation and that the idea behind dialogical modal logics should be pursued to its fullest. Thus, from a model-theoretic perspective, dialogical contexts will correspond to (names of) possible worlds. But one important difference is that in the dialogical framework the contexts are explicitly part of the players’ interaction through particle rules and through the special structural rule introduced below.