A General Multi-Agent Modal Logic K Framework for Game Tree Search

We present an application of Multi-Agent Modal Logic K (MMLK) to model dynamic strategy game properties. We also provide several search algorithms to decide the model checking problem in MMLK. In this framework, we distinguish between the solution concept of interest which is represented by a class of formulas in MMLK and the search algorithm proper. The solution concept defines the shape of the game tree to be explored and the search algorithm determines how the game tree is explored. As a result, several formulas class and several of search algorithms can represent more than a dozen classical game tree search algorithms for single agent search, two-player games, and multiplayer games. Among others, we can express the following algorithms in this work: depth-first search, Minimax, Monte Carlo Tree Search, Proof Number Search, Lambda Search, Paranoid Search, Best Reply Search.