  We aim to determine which temporal instance queries can be uniquely
characterised by a (polynomial-size) set of positive and negative temporal data
examples. We start by considering queries formulated in fragments of
propositional linear temporal logic LTL that correspond to conjunctive queries
(CQs) or extensions thereof induced by the until operator. Not all of these
queries admit polynomial characterisations but by restricting them further to
path-shaped queries we identify natural classes that do. We then investigate
how far the obtained characterisations can be lifted to temporal knowledge
graphs queried by 2D languages combining LTL with concepts in description
logics EL or ELI (i.e., tree-shaped CQs). While temporal operators in the scope
of description logic constructors can destroy polynomial characterisability, we
obtain general transfer results for the case when description logic
constructors are within the scope of temporal operators. Finally, we apply our
characterisations to establish (polynomial) learnability of temporal instance
queries using membership queries in the active learning framework.
