  Commonsense knowledge (CSK) about concepts and their properties is helpful
for AI applications. Prior works, such as ConceptNet, have compiled large CSK
collections. However, they are restricted in their expressiveness to
subject-predicate-object (SPO) triples with simple concepts for S and strings
for P and O. This paper presents a method called ASCENT++ to automatically
build a large-scale knowledge base (KB) of CSK assertions, with refined
expressiveness and both better precision and recall than prior works. ASCENT++
goes beyond SPO triples by capturing composite concepts with subgroups and
aspects, and by refining assertions with semantic facets. The latter is
essential to express the temporal and spatial validity of assertions and
further qualifiers. Furthermore, ASCENT++ combines open information extraction
(OpenIE) with judicious cleaning and ranking by typicality and saliency scores.
For high coverage, our method taps into the large-scale crawl C4 with broad web
contents. The evaluation with human judgments shows the superior quality of the
ASCENT++ KB, and an extrinsic evaluation for QA-support tasks underlines the
benefits of ASCENT++. A web interface, data, and code can be accessed at
https://ascentpp.mpi-inf.mpg.de/.
