Partially observed actions are observations of action executions in which we are uncertain about the identity of objects, agents, or locations involved in the actions (e.g., we know that action move(?o,?x,?y) occurred, but do not know ?o,?y). Observed-Action Reasoning is the problem of reasoning about the world state after a sequence of partial observations of actions and states. In this paper we formalize Observed-Action Reasoning, prove intractability results for current techniques, and find tractable algorithms for STRIPS and other actions. Our new algorithms update a representation of all possible world states (the belief state) in logic using new logical constants for unknown objects. A straightforward application of this idea is incorrect, and we identify and add two key amendments. We also present successful experimental results for our algorithm in Blocks-world domains of varying sizes and in Kriegspiel (partially observable chess). These results are promising for relating sensors with symbols, partial-knowledge games, multi-agent decision making, and AI planning.