We present the dialogical approach to logic, in a conceptual framework that, although deeply influenced by S. Rahman's work, is new in a number of respect. We show how to give in this framework a dialogical semantics for a variety of modal logics, relying on Gabbay's idea of a labelled deductive system. Such a dialogical semantics has enough expressive power to define dialogical games complete with respect to any first-order definable class of Kripke-style frames. In this context we propose to tackle the following question: given a modal formula, how can one define a first-order condition yielding a class of frames such that the formula is valid on it? There are some impossibility results from the literature that we will present, then we give an algorithm that will give a correct answer in all the simple cases. We claim that such an algorithm provides a different and hopefully interesting perspective on a notion that plays a role in the adaptive logics program, namely to gain insight about a (set of) formula(s).