  Not all properties are monitorable. This is a well-known fact, and it means
there exist properties that cannot be fully verified at runtime. However, given
a non-monitorable property, a monitor can still be synthesised, but it could
end up in a state where no verdict will ever be concluded on the satisfaction
(resp., violation) of the property. For this reason, non-monitorable properties
are usually discarded. In this paper, we carry out an in-depth analysis on
monitorability, and how non-monitorable properties can still be partially
verified. We present our theoretical results at a semantic level, without
focusing on a specific formalism. Then, we show how our theory can be applied
to achieve partial runtime verification of Linear Temporal Logic (LTL).
