  We consider state-based systems modelled as coalgebras whose type
incorporates branching, and show that by suitably adapting the definition of
coalgebraic bisimulation, one obtains a general and uniform account of the
linear-time behaviour of a state in such a coalgebra. By moving away from a
boolean universe of truth values, our approach can measure the extent to which
a state in a system with branching is able to exhibit a particular linear-time
behaviour. This instantiates to measuring the probability of a specific
behaviour occurring in a probabilistic system, or measuring the minimal cost of
exhibiting a specific behaviour in the case of weighted computations.
