In syntax, the theta criterion (in its original form) states that in a grammatical sentence, every theta role that a verb can assign must be realized by some argument, and each argument may bear only a single theta role.[1] So, for instance, for the verb send, which is associated with the theta-roles of Agent, Goal and Theme, a well formed sentence might look like this:
Here, the three theta roles are assigned to Robert, Mary and a package, respectively. The sentence would have been malformed if any of these arguments had been absent.
It is often noted that sometimes arguments of the verb are not overtly present, and that sometimes the verb may take more arguments than specified in the lexicon:
Linguists often explain sentences 2 and 3, where the verbs seem to be missing arguments, by positing a silent pronoun (pro) that occupies the phonologically empty argument positions. This can be justified by noting that one cannot get the meaning from sentence 2 that John ate something inedible, such as a rock, and that in sentence 3 there is a clear implied first-person subject.
In sentence 1, however, there is no clear theta-position that the death befitting a Roman soldier is occupying; it is unclear what licenses this cognate object, producing a pseudo-transitive use of the verb died. One plausible explication is the interpretation of the verb die in this phrase as synonym of suffer, undergo or be impaired; thus, the sentence may be interpreted as:
And then, the arguments are complete.