  In recent years, there has been an increasing interest in extending
traditional stream processing engines with logical, rule-based, reasoning
capabilities. This poses significant theoretical and practical challenges since
rules can derive new information and propagate it both towards past and future
time points; as a result, streamed query answers can depend on data that has
not yet been received, as well as on data that arrived far in the past. Stream
reasoning algorithms, however, must be able to stream out query answers as soon
as possible, and can only keep a limited number of previous input facts in
memory. In this paper, we propose novel reasoning problems to deal with these
challenges, and study their computational properties on Datalog extended with a
temporal sort and the successor function (a core rule-based language for stream
reasoning applications).
