  General-purpose knowledge bases (KBs) are a cornerstone of knowledge-centric
AI. Many of them are constructed pragmatically from Web sources, and are thus
far from complete. This poses challenges for the consumption as well as the
curation of their content. While several surveys target the problem of
completing incomplete KBs, the first problem is arguably to know whether and
where the KB is incomplete in the first place, and to which degree.
  In this survey we discuss how knowledge about completeness, recall, and
negation in KBs can be expressed, extracted, and inferred. We cover (i) the
logical foundations of knowledge representation and querying under partial
closed-world semantics; (ii) the estimation of this information via statistical
patterns; (iii) the extraction of information about recall from KBs and text;
(iv) the identification of interesting negative statements; and (v) relaxed
notions of relative recall.
  This survey is targeted at two types of audiences: (1) practitioners who are
interested in tracking KB quality, focusing extraction efforts, and building
quality-aware downstream applications; and (2) data management, knowledge base
and semantic web researchers who wish to understand the state of the art of
knowledge bases beyond the open-world assumption. Consequently, our survey
presents both fundamental methodologies and their working, and gives
practice-oriented recommendations on how to choose between different approaches
for a problem at hand.
