The study on complex object data model and its logic data language has received a lot of attention in recent years. In this paper, a complex object data model COMis proposed, and the syntax of its declarative query language, called CO-DATAI.OG, ispresented. In the respect of semantics, the concepts such as universe, base, interpretation, satisfaction, and model are defined, then based on the lattice property of COM Instances the model intersection theorem, the theorem on existence of the least model, andthe fixpoint characteristic of the least model are proved. Therefore the semantic theoreticalframework is reconstructed.