  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. Solving the
composition problem is fundamental for the dialogical approach to logic;
despite its simplicity, it often requires an indirect solution with the help of
significant logical machinery such as cut-elimination. We give a set N of
dialogue rules that is quite close to a set of rules known to characterize
classical propositional logic, and which is evidently well-justified from the
dialogical point of view, but whose set of dialogically valid formulas is quite
peculiar (and non-trivial). Its peculiarity notwithstanding, the composition
problem for N can be solved directly.
