This work focuses on the licensing conditions and logical structure of understood-argument constructions, or complement-drop constructions, in English. There are two main types of such arguments: Indefinite Understood Arguments (IUA) and Definite Understood Arguments (DUA). IUA readings occur in such cases in He ate, He cooked. In such cases, the reference of the dropped element need not be known for the sentence to be satisfactorily interpretable. DUA readings are given in such examples as She followed, She won. Here the reference of the missing element must be known to the speaker/hearer; it must appear in discourse.

Our central claim is that it is not necessary to resort to explanatory factors outside the lexical-semantic structure of verbs in order to account for the alternations. We propose that for both IUA and DUA, the structure of the understood argument is a complex structure involving existential quantification: "∃x [P(x)]". It is never a simplex, atomic element that could be represented by an individual constant. For IUA cases, we justify this complex structure by showing that it is mirrored in the structure of the alternating verbs. We note in particular that IUA verbs often undergo other alternations such as the material/product alternation, which we consider to be an indication of a complex lexical structure.

For Definite Understood Arguments, we give two licensing factors that correspond to the variable and the predicate in the logical form. We motivate existential quantification in DUA constructions, by considering such contrasts as I know/I know about that vs. I believe/*I believe about that. Selecting for a PP-complement correlates with the possibility of DUA. We claim that in this example, the about-phrase provides a slot for a variable, since the phrase makes allusion to some object without stating explicitly what it is.

We conclude by analyzing subject-drop alternations–the causative-inchoative alternation–in the light of our findings regarding complement drop. We note that this alternation occurs with verbs of a simplex structure; and we offer a description of the general system of argument drop in English.