Probabilistic reasoning, fuzzy logic, modal logic, neighborhood semantics, matrix game

In this contribution we apply fuzzy neighborhood semantics to multiple agents' reasoning about each other's subjective probabilities, especially in game-theoretic situations. The semantic model enables representing various game-theoretic notions such as payoff matrices or Nash equilibria, as well as higher-order probabilistic beliefs of the players about each other's choice of strategy. In the proposed framework, belief-dependent concepts such as the strategy with the best expected value are formally derivable in higher-order fuzzy logic for a large class of matrix games.