  In complex reasoning tasks, as expressible by Answer Set Programming (ASP),
problems often permit for multiple solutions. In dynamic environments, where
knowledge is continuously changing, the question arises how a given model can
be incrementally adjusted relative to new and outdated information. This paper
introduces Ticker, a prototypical engine for well-defined logical reasoning
over streaming data. Ticker builds on a practical fragment of the recent
rule-based language LARS which extends Answer Set Programming for streams by
providing flexible expiration control and temporal modalities. We discuss
Ticker's reasoning strategies: First, the repeated one-shot solving mode calls
Clingo on an ASP encoding. We show how this translation can be incrementally
updated when new data is streaming in or time passes by. Based on this, we
build on Doyle's classic justification-based truth maintenance system (TMS) to
update models of non-stratified programs. Finally, we empirically compare the
obtained evaluation mechanisms. This paper is under consideration for
acceptance in TPLP.
