Dynamic Logic on Games with Structured Strategies

We consider a propositional dynamic logic whose programs are regular expressions over game strategy pairs. At the atomic level, these are finite extensive form game trees with structured strategy specifications, whereby a player’s strategy may depend on properties of the opponent’s strategy. The advantage of imposing structure not merely on games or on strategies but on game strategy pairs, is that we can speak of a composite game g followed by g′ whereby if the opponent played a strategy s in g, the player responds with s′ in g ′ to ensure a certain outcome. In the presence of iteration, a player has significant ability to strategise taking into account the explicit structure of games. We present a complete axiomatization of the logic and prove its decidability. The tools used combine techniques from PDL, CTL and game logics.