  Argumentation accommodates various rhetorical devices, such as questions,
reported speech, and imperatives. These rhetorical tools usually assert
argumentatively relevant propositions rather implicitly, so understanding their
true meaning is key to understanding certain arguments properly. However, most
argument mining systems and computational linguistics research have paid little
attention to implicitly asserted propositions in argumentation. In this paper,
we examine a wide range of computational methods for extracting propositions
that are implicitly asserted in questions, reported speech, and imperatives in
argumentation. By evaluating the models on a corpus of 2016 U.S. presidential
debates and online commentary, we demonstrate the effectiveness and limitations
of the computational models. Our study may inform future research on argument
mining and the semantics of these rhetorical devices in argumentation.
