We present a trainable sequential-inference technique for processes with large state and observation spaces and relational structure. Our method assumes "reliable observations", i.e., that each process state persists long enough to be reliably inferred from the observations it generates. We introduce the idea of a "state-inference function" (from observation sequences to underlying hidden states) for representing knowledge about a process and develop an efficient sequentialinference algorithm, utilizing this function, that is correct for processes that generate reliable observations consistent with the state-inference function. We describe a logical representation for state-inference functions in relational domains and give a corresponding supervised learning algorithm. Empirical results, in relational video interpretation, show that the resulting trainable system provides significantly improved accuracy and speed relative to a variety of recent, hand-coded, non-tr...