Strategies in Sabotage Games: Temporal and Epistemic Perspectives
For researchers in modal logic and dynamic graph theory, this provides a new formal framework for analyzing sabotage games, but it is an incremental extension of existing logics.
The paper proposes using alternating time temporal logic (ATL*) and its epistemic extensions to reason about winning strategies in sabotage games, where a runner tries to reach a goal while a demon removes edges. This framework enables reasoning about temporal properties of dynamic graphs.
Sabotage games are played on a dynamic graph, in which one agent, called a runner, attempts to reach a goal state, while being obstructed by a demon who at each round removes an edge from the graph. Sabotage modal logic was proposed to carry out reasoning about such games. Since its conception, it has undergone a thorough analysis (in terms of complexity, completeness, and various extensions) and has been applied to a variety of domains, e.g., to formal learning. In this paper, we propose examining the game from a temporal perspective using alternating time temporal logic (ATL$^\ast$), and address the players' uncertainty in its epistemic extensions. This framework supports reasoning about winning strategies for those games, and opens ways to address temporal properties of dynamic graphs in general.