Dialogue games are two-player logic games between a Proponent who puts
forward a logical formula A as valid or true and an Opponent who disputes this.
An advantage of the dialogical approach is that it is a uniform framework from
which different logics can be obtained through only small variations of the
basic rules. We introduce the composition problem for dialogue games as the
problem of resolving, for a set S of rules for dialogue games, whether the set
of S-dialogically valid formulas is closed under modus ponens.