  Arguments often do not make explicit how a conclusion follows from its
premises. To compensate for this lack, we enrich arguments with structured
background knowledge to support knowledge-intense argumentation tasks. We
present a new unsupervised method for constructing Contextualized Commonsense
Knowledge Graphs (CCKGs) that selects contextually relevant knowledge from
large knowledge graphs (KGs) efficiently and at high quality. Our work goes
beyond context-insensitive knowledge extraction heuristics by computing
semantic similarity between KG triplets and textual arguments. Using these
triplet similarities as weights, we extract contextualized knowledge paths that
connect a conclusion to its premise, while maximizing similarity to the
argument. We combine multiple paths into a CCKG that we optionally prune to
reduce noise and raise precision. Intrinsic evaluation of the quality of our
graphs shows that our method is effective for (re)constructing human
explanation graphs. Manual evaluations in a large-scale knowledge selection
setup confirm high recall and precision of implicit CSK in the CCKGs. Finally,
we demonstrate the effectiveness of CCKGs in a knowledge-insensitive argument
quality rating task, outperforming strong baselines and rivaling a GPT-3 based
system.
