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Real-world robot task planning is intractable in part due to partial observability. A common approach to reducing complexity is introducing additional structure into the decision process, such as mixed-observability, factored states, or temporally-extended actions. We propose the locally observable Markov decision process, a novel formulation that models task-level planning where uncertainty pertains to object-level attributes and where a robot has subroutines for seeking and accurately observing objects. This models sensors that are range-limited and line-of-sight—objects occluded or outside sensor range are unobserved, but the attributes of objects that fall within sensor view can be resolved via repeated observation. Our model results in a three-stage planning process: first, the robot plans using only observed objects; if that fails, it generates a target object that, if observed, could result in a feasible plan; finally, it attempts to locate and observe the target, replanning after each newly observed object. By combining LOMDPs with off-the-shelf Markov planners, we outperform state-of-the-art solvers for both object-oriented POMDP and MDP analogues with the same task specification. We then apply the formulation to successfully solve a task on a mobile robot.