This paper studies the learning of task constraints that allow grasp generation in a goal-directed manner. We show how an object representation and a grasp generated on it can be integrated with the task requirements. The scientific problems tackled are (i) identification and modeling of such task constraints, and (ii) integration between a semantically expressed goal of a task and quantitative constraint functions defined in the continuous object-action domains. We first define constraint functions given a set of object and action attributes, and then model the relationships between object, action, constraint features and the task using Bayesian networks. The probabilistic framework deals with uncertainty, combines apriori knowledge with observed data, and allows inference on target attributes given only partial observations. We present a system designed to structure data generation and constraintvlearning processes that is applicable to new tasks, embodiments and sensory data. The application of the task constraint model is demonstrated in a goal-directed imitation experiment.