This test is based on the assumption that the words "do so" can be used to substitute for a VP. By using the test we can determine which sequences of words are VP constituents. Once we know which sequences are VPs, we can also determine which phrases are arguments and modifiers.
Consider a sentence like
Now let's apply the "do so" test to the following sequences of phrases, to see which, if any of them, are VPs.
To test these, we create sentences like the following, in which "do so" replaces the sequence that we're testing.
Based on our judgments on the sentences above, we conclude the following:
So, we have a situation where two sequences, one larger than the other, both behave as if they are VPs, and two smaller sequences behave as if they are not VPs. This indicates that the smallest VP in the structure (which we could call the "nuclear" VP) is
This could be generated by the rule
which indicates that the NP "the magic bean" and the PP "in the box" are arguments of the verb.
On the other hand, the PP "before dinner" combines with a VP to create a larger VP. This must therefore have been created using the VP-modifier rule
which indicates that the PP "before dinner" is a modifier.
Notice that this argument is based on the following assumption about how arguments and modifiers are arranged.
You will have noticed that in the Trees program, the entries for verbs are often associated with slots for NPs or PPs which they must appear with. These are the arguments of the verb, and these always appear within the nuclear VP. On the other hand, the entirely optional modifier phrases are always attached to VP using the VP modifier rule.
You might be wondering why we don't simply determine what is an argument and what is a modifier of the verb based on whether or not a phrase is optional. In the example above using "put", this test would have given the same results. The PP "before dinner" is optional, but the other phrases could not be omitted without leading to ungrammaticality.
Unfortunately, though, optionality is not always a reliable test of whether a phrase is an argument, because there are some verbs which have optional arguments. The verb "eat" is an example of this. We can use it as a transitive verb, or as an intransitive verb, as in the following:
The goblins ate.
The goblins ate the candy.
This optionality of the object NP might lead us to think that it is a modifier. However, there is a clear intuition that the NP appearing after "eat" refers to an essential part of an eating event, which is a characteristic of arguments. This intuition is supported by the "do so" test, which shows that "do so" cannot replace "ate" alone in a sentence containing an object NP.
The goblins ate the candy, and the pixies did so (too).
*The goblins ate the candy, and the pixies did so the cake.
Therefore, the "do so" test seems to provide a more reliable test of arguments vs. modifiers than the optionality test.