Practical Grammar 7

Prepositional Phrases: explaining the complex annotation

The textbook contains a c-structure rule for VP like the following:

1. VP → V          PP
       ↑=↓   (↑ (↓ PCASE)) = ↓

which translates into the following xlfg rule:

1. VP → V PP
2. {
3. ↑=↓1;
4. (↑ (↓2 PCASE)) = ↓2;
5. }

Explaining the meaning of (↑ (↓ PCASE)) = ↓

The annotation on the PP looks a lot scarier than it actually is! Let us look at its structure piece by piece. To do this, we will begin by looking at the annotations in the following rule one more time:

1. VP → V DP
2. {
3. ↑=↓1;
4. (↑ OBJ) =↓2;
5. }

Remember that by definition

• ↑ is "the mother's f-structure" and
• ↓2 refers to "the f-structure of daughter 2"

So, in the tree licensed by the rule above ↑ is the VP's f-structure. Let us call that f_VP. And ↓2 refers to the DP's f-structure. Let us correspondingly call that f_DP. With that, the formula (↑ OBJ) =↓2 becomes

(fVP OBJ) = fDP

Given the following:

(fVP OBJ) = the value of the attribute OBJ in the f-structure of the VP

(f_VP OBJ) = f_DP means:

The value of the attribute OBJ in the f-structure of the VP (= fVP) is the f-structure of the DP (= fDP).

This translates into the following graphical representation:

[fVPOBJ   [fDP ]]

In other words, all the functional information associated with the PP daughter describes the OBJ of the VP.

With this understanding, let us now look at the rule

1. VP → V PP
2. {
3. ↑=↓1;
4. (↑ (↓2 PCASE)) = ↓2;
5. }

Replacing the up and down arrows in 4. by contant names yields the following:

(fVP (fPP PCASE)) = fPP

We can restate this formula as follows:

(fVP X) = fPP and X = (fPP PCASE)

When we break down the formula like this, we get two expressions:

1.(f_VP X) = f_PP
2. X = (f_PP PCASE)

We know the meanings of these formulas. Let us represent them in graphical form:

1'. [_fVP X   [_fPP ]]]
2'.

[_fVPOBJ   [_fDP ]]