Modal logics of sabotage revisited

Sabotage modal logic was proposed in 2003 as a format for analysing games that modify graphs they are played on. We investigate some model-theoretic and proof-theoretic aspects of sabotage modal logic, which has come to be viewed as an early dynamic logic of graph change. Our first result is a characterization theorem for sabotage modal logic as a fragment of first-order logic which is invariant with respect to a natural notion of 'sabotage bisimulation'. Next, we offer a sound and complete tableau method and its associated labelled sequent calculus for analysing reasoning in sabotage modal logic. Finally, we identify and briefly explore a number of open research problems concerning sabotage modal logic that illuminate its complexity, placing it within the current landscape of modal logics that analyse model update, and, returning to the original motivation of sabotage, fixed-point logics for network games.