  Inferential models have recently gained in popularity for valid uncertainty
quantification. In this paper, we investigate inferential models by exploring
relationships between inferential models, fiducial inference, and confidence
curves. In short, we argue that from a certain point of view, inferential
models can be viewed as fiducial distribution based confidence curves. We show
that all probabilistic uncertainty quantification of inferential models is
based on a collection of sets we name principle sets and principle assertions.
