This paper presents a general query language for conceptual graphs. First, we introduce kernel query graphs. A kernel query graph can be used to express an "or" between two sub-graphs, or an "option" on an optional sub-graph. Second, we propose a way to express two kinds of queries (ask and select) using kernel query graphs. Third, the answers of queries are computed by an operation based on graph homomorphism: the projection from a kernel query graph.