In the theory of abstract interpretation, we introduce the
observational completeness, which extends the common notion of
completeness. A domain is complete when abstract computations are as
precise as concrete computations. A domain is observationally complete
for an observable $\pi$ when abstract computations are as precise as
concrete computations, if we only look at properties in $\pi$. We
prove that continuity of state-transition functions ensures the
existence of the least observationally complete domain. When
state-transition functions are additive, the least observationally
complete domain boils down to the complete shell.