We present a technique for transferring query optimization techniques, developed for relational databases, into object databases. We demonstrate this technique for ODMG database schemas defined in ODL, and for object queries expressed in OQL. The object schema is represented using a logical representation (Datalog). Semantic knowledge about the object data model, e.g., class hierarchy information, relationship between objects, etc., as well as semantic knowledge about the particular schema and application domain, are expressed as integrity constraints. An OQL object query is represented as a logic query, and query optimization is performed in the Datalog representation. We obtain equivalent (optimized) logic queries, and subsequently obtain equivalent (optimized) OQL queries, for each equivalent logic query. In this paper, we present one optimization technique for semantic query optimization (SQO), based on the residue technique. We show that our technique generalizes previous research on SQO for object databases. We handle a large class of OQL queries, including queries with constructors and methods. We demonstrate how SQO can be used to eliminate queries which contain contradictions and simplify queries, e.g., by eliminating joins, or by reducing the access scope for evaluating a query to some specific subclasss(es). We also demonstrate how the definition of a method, or integrity constraints describing the method, can be used in optimizing a query with a method.