In household and retail store environments, humans efficiently identify grasp regions of an object to perform everyday tasks. To enable robots to understand the requirements of a task and the properties of an object, a novel grasp framework, called the Shape Primitive and Reasoning Grasping Engine (SPaRGE), is proposed in this thesis. SPaRGE combines a data-driven approach, a superquadric algorithm, and a logic-based approach to find task-specific object grasp poses from a partial point cloud. Multiple grasp poses are recovered using the data-driven approach, while objects are represented as multiple primitive shapes using the superquadric algorithm and logic-based approach. Logic rules are used to decide which primitive shape meets the criteria of a given task, resulting in a primitive shape indicating a grasp region. The data-driven approach then finds a grasp pose that meets the task requirements. Two versions of the logic-based approach are presented, differing in their design choices that affect the generalizability and scalability of the logic rules. The SPaRGE framework is evaluated on common household and retail store objects, demonstrating an average true positive rate of 81.2% and 86.0%, respectively, in enabling a robot to grasp objects at a desired region. Results show that the SPaRGE framework enables real-time object grasping without prior knowledge of the objects. Further experiments show that the SPaRGE framework can be adapted successfully for real-world object grasping scenarios. The proposed framework provides a significant contribution toward enabling robots to perform human-like grasping in real-world environments.