While grasps must satisfy the grasping stability criteria, good grasps depend on the specific manipulation scenario: the object, its properties and functionalities, as well as the task and grasp constraints. In this paper, we consider such information for robot grasping by leveraging manifolds and symbolic object parts. Specifically, we introduce a new probabilistic logic module to first semantically reason about pre-grasp configurations with respect to the intended tasks. Further, a mapping is learned from part-related visual features to good grasping points. The probabilistic logic module makes use of object-task affordances and object/task ontologies to encode rules that generalize over similar object parts and object/task categories. The use of probabilistic logic for task-dependent grasping contrasts with current approaches that usually learn direct mappings from visual perceptions to task-dependent grasping points. We show the benefits of the full probabilistic logic pipeline experimentally and on a real robot.