Assembly recipes can elegantly be represented in description logic theories. With such a recipe, the robot can figure out the next assembly step through logical inference. However, before performing an action, the robot needs to ensure various spatial constraints are met, such as that the parts to be put together are reachable, non occluded, etc. Such inferences are very complicated to support in logic theories, but specialized algorithms exist that efficiently compute qualitative spatial relations such as whether an object is reachable. In this work, we combine a logic-based planner for assembly tasks with geometric reasoning capabilities to enable robots to perform their tasks under spatial constraints. The geometric reasoner is integrated into the logic-based reasoning through decision procedures attached to symbols in the ontology.