: Fuzzy Cognitive Maps (FCMs) can represent and reason causal knowledge with stronger semantics. And the causal knowledge widely exists in Knowledge Grid. To provide information services with stronger semantics in Knowledge Grid, we need to know the reasoning mechanism and the characteristics of FCMs. In this paper, we have proved that the reasoning process of FCMs is a discrete topological semi-dynamic system. This theory can help us analyze the reasoning process and find the new characteristics of FCMs, which can guide us using FCMs to provide intelligent information services flexibly in Knowledge Grid.