Starting Small

The constituency tests that we performed in the last chapter allowed us to see that every sentence is made up of smaller units of the sentence. Importantly, each constituent forms its own “semantic” unit as well. This is sometimes difficult to understand, and even harder to demonstrate, so we’ll start first by looking at a somewhat “smaller” problem, and work up to full sentences.

English (like all Germanic languages) has a productive process through which new words can be formed that involves putting two words together. The resulting words are called compounds.

This process is, theoretically, infinitely recursive, meaning that we can continue to make new words from existing words.

We can think of each piece of a compound as a constituent. Rice-pot has two pieces of meaning,  rice and pot. When we put them together, we make something whose meaning is the combination of both. This idea is represented in terms of bracketing structure.

Inside each pair of brackets is one meaning “unit.” So rice-pot involves three pairs of brackets: one around rice, one around pot and one around the compound rice-pot. Same with swan-boat.

This way of representation allows us to iteratively represent more complex compounds, as in (2).

When we build larger compounds, we are creating a meaningful unit, and then adding to it. So first I create the word rice-pot, and it has a meaning like, “a pot for rice.” Then I create the word rice-pot-rack, which has the meaning “a rack for a pot for rice.” In other words, the meaning of the entire word depends on the meaning of its parts.

Of course, the more complex our compounds become, the more difficult it is to read the bracketing structure. So another way to express the exact same information is by using a tree, as in (3).

Each node in the tree corresponds to one pair of brackets. Thus, trees and brackets provide the exact same amount of information, it’s just that trees do it in a visually more appealing way. But it’s always possible to state a bracketing structure as a tree, and vice versa.

I can actually make my representations slightly more informative by adding in category information. The following trees and bracketing structures give us all the preceding information, and they additionally tell us what the category of each constituent is.

Note that it’s not necessary to explicitly state the compound words that are formed at each junction, because I can just look lower in the tree to figure out what that word is. The reason it’s good to list the category, though, is that you can combine more than one category. We therefore want to know which category “projects,” that is, names the resulting word.

Scaling up to sentences

Just like each word in a compound is a unit of meaning, which combine to create bigger meanings, sentences also behave the same way. Each constituent contributes a piece of meaning. The constituents combine to create larger meanings, until the sentence is complete.

Our constituency tests are telling us how the pieces of meaning come together. Just like we know that the compound sweet potato chickpea salad is made up of two smaller compounds sweet potato and chickpea salad, sentences can be broken up into smaller chunks. For instance, we found that in the sentence The tired doctor slept, the string of words the tired doctor is a constituent. Thus, this piece of meaning is enclosed in brackets or corresponds to a single node in a tree.

And just like with compounds, we can also add in information about categories. The constituent the tired doctor is a Determiner Phrase (for reasons that we’ll discuss in chapter 5), and the whole thing is a Sentence_English (abbreviated S_E).

Here comes the crucial leap to phrase structure grammars. The rules of a phrase structure grammar are the possible structures in a language. That is, the phrase structure grammars tell you what the possible bracketing structures and trees are in a language. Consider again our rules for English from chapter 2 (now with abbreviations).

These phrase structure rules tell you how information is packaged in English. That is, they tell that the phrase [_DP … ] precedes V. And they tell you that inside of DP you can have either [_DP D N ] or [_DP D A N ]. More generally, the three phrase structure rules say the following are the (only) possible trees and bracketing structures in English.

Phrase structure grammars are thus “instructions” for what trees/bracketing structures can be drawn in a language. Our fragment for English above is quite limited; it only generates a few trees/structures. We will expand on this fragment in the following chapter.

Structural Ambiguity

What does the following compound mean?

Many of you will say that it means, “someone who plants baby trees.” And many of you will say that it means “a tree-planter who is a baby.” Both of these are right; it’s possible to get both readings of the compound.

If we wanted to represent each meaning, we would choose different structures. The “baby-trees” meaning would have the following representations.

The reason is that we want “baby tree” to be a unit of meaning, i.e., a constituent, because that meaning describes the kind of planter it is.

On the other hand, the “tree-planting-baby” meaning would have the following representation

The reason is that we want “tree-planter” to be a unit of meaning first, because ultimately we’re describing a kind of tree-planter.

This kind of ambiguity is called structural ambiguity, because we can represent the ambiguity structurally.

The take-away point here is that different meanings correspond to different structures. More abstractly, the different meanings are the result of packaging the information in different ways.

The same is true when we scale up to full trees. Consider the following (very famous) sentence in English.

This sentence is ambiguous as well. On the one hand, it can mean that Mary saw a man who was holding binoculars. On the other hand, it can mean that Mary used binoculars to see the man. In the first meaning with the  binoculars describes a property of the man. On the second meaning, with the binoculars describes how Mary is “seeing.”

Just like baby-tree-planter, we observe different meanings. We can ask then whether those meanings correspond to different structures. The way to answer this question is to apply constituency tests, because constituency tests tell us how the parts of a sentence fit together. For instance, let’s apply the substitution test. Specifically what I’m doing in this test is trying to see if with the binoculars must connect with the other words in a particular way, in particular, if it must modify man.

Notice first that both of these sentences are grammatical. At first, you might be tempted to think that we’ve done our test wrong, since the results of (17) and (18) suggest that there are two ways to do the constituency of this sentence. But in fact, if we applied all of our tests, we’d find that both underlined strings of words are possible constituents. What is crucial is that the constituent parsings in (17) and (18) correspond to a different meanings. This is the hallmark of a structural ambiguity: different meanings correlate with different structures.

Explicitly, what (17) and (18) shows is that once we’ve applied a test, then the ambiguity goes away. When we force [ man with the binoculars ] to be a constituent by replacing that string with him, the sentence can only mean that the man has the binoculars. In contrast, when we force [ the man ] to be a constituent by replacing just that string with him, then the sentence can only mean that Mary was using binoculars. This is because by applying the test, we’re forcing the sentence to have a certain structure, and therefore to have a certain meaning.

Again, the take-away message here is: different meanings have different structures—and vice versa.

Where we’re going

With these representational tools, brackets and trees, we’re going to try to build a functional description of a language using phrase structure rules. What is important is that our description—that is the phrase structure grammar—accurately represents the language in question. To do this we simply use the tools we have: constituency and category diagnostics.