  Juba recently proposed a formulation of learning abductive reasoning from
examples, in which both the relative plausibility of various explanations, as
well as which explanations are valid, are learned directly from data. The main
shortcoming of this formulation of the task is that it assumes access to
full-information (i.e., fully specified) examples; relatedly, it offers no role
for declarative background knowledge, as such knowledge is rendered redundant
in the abduction task by complete information. In this work, we extend the
formulation to utilize such partially specified examples, along with
declarative background knowledge about the missing data. We show that it is
possible to use implicitly learned rules together with the explicitly given
declarative knowledge to support hypotheses in the course of abduction. We
observe that when a small explanation exists, it is possible to obtain a
much-improved guarantee in the challenging exception-tolerant setting. Such
small, human-understandable explanations are of particular interest for
potential applications of the task.
