  Research on summarization has mainly been driven by empirical approaches,
crafting systems to perform well on standard datasets with the notion of
information Importance remaining latent. We argue that establishing theoretical
models of Importance will advance our understanding of the task and help to
further improve summarization systems. To this end, we propose simple but
rigorous definitions of several concepts that were previously used only
intuitively in summarization: Redundancy, Relevance, and Informativeness.
Importance arises as a single quantity naturally unifying these concepts.
Additionally, we provide intuitions to interpret the proposed quantities and
experiments to demonstrate the potential of the framework to inform and guide
subsequent works.
