Abstract: Knowledge representation and reasoning is a key issue of the Knowledge Grid. This paper proposes a Knowledge Map (KM) model for representing and reasoning causal knowledge as an overlay in the Knowledge Grid. It extends Fuzzy Cognitive Maps (FCMs) to represent andreason not only simple cause-effect relations, but also time-delaycausal relations, conditional probabilistic causal relations andsequential relations. The mathematical model and dynamic behaviors ofKM are presented. Experiments show that, under certain conditions, thedynamic behaviors of KM can translate between different states. Knowingthis condition, experts can control or modify the constructed KM whileits dynamic behaviors do not accord with their expectation. Simulationsand applications show that KM is more powerful and natural than FCM inemulating real world.