arXiv:2610.09358v1 Announce Type: new Abstract: Robots are increasingly expected to provide personalized services in everyday environments. To do so, they must ground natural-language commands such as "Where is my backpack?" or "Find my bottle" and execute them by reasoning about object instances, people, locations, and ownership. This is challenging because ownership is rarely labeled explicitly and must be inferred from long-term, behavioral evidence of human-object interactions. To address this, we present COOL, a novel robotic framework for autonomously learning object ownership from everyday observations and maintaining a long-term spatial memory of its environment. To keep its memory current, COOL uses an agent-based curiosity-driven data collection strategy that guides the robot toward the most promising locations to gain information and refresh stale observations. Offline experiments, ablation studies, and real-world evaluations show that COOL can infer ownership relations from real-world interactions and use this knowledge for ownership-conditioned navigation and task execution.