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We study stream reasoning in DatalogMTL —an extension of Datalog with metric temporal operators. We propose a sound and complete stream reasoning algorithm that is applicable to forward-propagating DatalogMTL programs, in which propagation of derived information towards past time points is precluded. Memory consumption in our generic algorithm depends both on the properties of the rule set and the input data stream; in particular, it depends on the distances between timestamps occurring in data. This may be undesirable in certain practical scenarios since these distances can be very small, in which case the algorithm may require large amounts of memory. To address this issue, we propose a second algorithm, where the size of the required memory becomes independent on the timestamps in the data at the expense of disallowing punctual intervals in the rule set. We have implemented our approach as an extension of the DatalogMTL reasoner MeTeoR and tested it experimentally. The obtained results support the feasibility of our approach in practice. [ABSTRACT FROM AUTHOR]