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5.7: Trees- Introducing X-bar theory

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    • Catherine Anderson, Bronwyn Bjorkman, Derek Denis, Julianne Doner, Margaret Grant, Nathan Sanders, and Ai Taniguchi
    • eCampusOntario

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    Constituency tests and phrase structure rules provide a useful starting point for thinking about the structure of possible sentences, but they don’t really start explaining why certain structures are grammatical, or predicting what possible and impossible grammars might look like. In this section we introduce X-bar theory, which aims to make stronger predictions by restricting the shape of possible trees. It’s called that because it introduces an extra layer of structure inside phrases called the “bar level”.

    To see why we might want to constrain what trees are possible, let’s begin by thinking about a type of structure that’s really easy to describe using a phrase structure rule:

    • Weird phrase structure rule: NP –> V (Adj) PP

    This rule is weird because it’s a noun phrase that’s missing the noun: we already saw in Section 6.3 is that what makes something a noun phrase is precisely that it has a noun inside it. The restriction that all natural languages phrases have heads of the same category is the first limit we’ll put on possible structures in X-bar theory:

    • Every phrase (XP) has a head of the same category (X)

    And this goes the other way as well: all heads (words) project (or “occur inside”) a phrase of their category:

    • Every head (X) projects a phrase of the same category (XP)

    What this means is that even when a noun or verb—or any other category—doesn’t obviously have any other words in the same phrase as it, it’s still inside an NP or a VP. In other words, while the two sentences in (1) are in one sense very different (one has two words, the other has 11), in another sense they have the same structure: both sentences consist of an NP followed by a VP.

    (1) a. Cats sleep.
    b. The many very fast spaceships carried a lot of valuable cargo.

    By default, in X-bar theory we assume that the same constraints apply to all categories and phrases, and that they apply in all languages. In the absence of evidence to the contrary, we assume that determiners occur inside determiner phrases (DPs), degree words occur inside degree phrases (DegPs), and so on.

    The assumption that all phrases involve the same structure, and that this is true in all languages, is a hypothesis. If we encounter evidence that is inconsistent with this hypothesis, we would revise the theory to account for new data. Active research in syntax consists of investigating grammatical patterns in languages, and showing how they do (or do not) require specific revisions to current syntactic theories.

    The key feature of X-bar theory (and the source of its name) arises from the observation that phrases aren’t just a flat structure.

    Our phrase structure rule for NPs, for example, could build NPs that contain a determiner (or DP), a noun, and a PP, but there was no sub-grouping. The tree diagram in Figure 6.5 shows this. (the triangle over robots indicates that we have abbreviated structure inside this constituent.)

    Tree diagram: [NP [ Det \\ a ] [ N \\ picture ] [ PP [ [ P \\ of ] [NP [robots ] ] ] ] ]
    Figure 6.5 Tree diagram for [a picture of robots]

    What we find if we look at phrases of all types, in many languages, is that head is always in a closer relationship with one other element inside the phrase, than with anything else. Specifically, heads are in a closer relationship with their complement—remember that in English the complement follows the head of the phrase, while it can come before the head in other languages. We saw in Section 6.3, for example, that verbs determine whether and how many objects they combine with. Above we saw that adjectives generally combine with PP complements, but that a few adjectives idiosyncratically allow NP complements.

    This means that there are units—constituents—inside phrases. So not only do all heads have phrases, and all phrases have heads, but there is what we might call a “mid sized sub-phrase” in every phrase (or an “intermediate phrase”). This mid-sized phrase is called X-bar (written X’), which is where the theory gets its name.

    So we expand X-bar theory to the following generalizations, expressed in phrase structure rules:

    • XP → (YP) X’
    • X’ → X (ZP)

    XP, YP, and ZP are all variables over any category of phrase. These rules can be read as saying:

    Every phrase (XP) must have a bar-level of the same category (X’) within it, optionally preceded by another phrase (YP). Every bar-level (X’) must have a head of the same category within it, optionally followed by another phrase (ZP).

    The positions occupied by YP and ZP are argument positions, and they have special names. The names for structural relations in trees are adapted from family relationships: parent, child, etc.

    The sibling of the head is the copmlement (with an “e”), not the compliment (with an “i”)! This is complement as in set theory, not as in saying nice things to someone.
    Sibling of the head X (child of X’) is its complement
    Heads select their complement (including if they take a complement)
    The child of XP, sister of X’ is the specifier of the phrase

    If we put these labels in the tree in place os “YP” and “ZP” above, we get a general X-bar template for English (specific to English because it includes the linear order found in English).

    X-bar schema for English: [ XP [ (Specifier) ] [ X' [ X ] [ (Complement) ] ] ]
    Figure 6.6 Generalized X-bar template (for English, head initial)

    What is the evidence for bar levels? In the remainder of this section we review the evidence for sub-constituents inside NPs and VPs.

    Evidence for N’

    The evidence for N’ (“N-bar”) involves showing that a noun is in a closer relationship with a PP that follows it than it is with a previous determiner.

    We can show this with constituency tests that target this sub-NP unit. These tests are a bit trickier to apply than the constituency tests covered in Section 6.4, but they follow the same general principle.

    Here we will only go through one of these tests: one-replacement. Just as a pronoun can replace a whole NP, the word “one” can (for at least some speakers of English) replace a noun and a following prepositional phrase, leaving behind anything before the noun. Like other kinds of replacement, especially replacement with do for VPs, one-replacement requires that there’s an earlier NP that “fills in” what’s being replaced.

    (2) [NP Yesterday’s launch of a spaceship ] was exciting, but [ today’s one ] was not. (where [one]=[launch of a spaceship])

    By contrast, you can’t replace a determiner and an N with one, leaving the PP behind:

    (3) *[NP The launch of a spaceship ] is exciting, but [ one of a mining drone ] is not. (where [one]=[the launch])
    Recall from Section 6.5 that determiners and possessors are in complementary distribution, which we account for by putting them in the same structural position: NP only has one specifier, so it can only hold one determiner or possessor.

    This gives us the following overall structure of an NP, showing a closer relationship between the N and a following PP than between either of those and the preceding determiner or possessor.

    Tree diagram: [ NP [ NP [ yesterday’s ] ] [ N' [ N [launch] ] [ PP [P' [P [of] ] [NP [a spaceship] ] ] ] ] ]
    Figure 6.7 Tree diagram for [ yesterday’s launch of a spaceship ]

    Evidence for V’

    We can do similar tests to find a constituent inside VP, consisting of the verb and its object. For example, we can elide a verb and its object, leaving a previous AdvP behind, but we cannot elide AdvP + V, leaving the NP object behind.

    (4) a. They will [VP quickly build a spaceship], and we will [VP slowly _ ]
    b. *They will [VP quickly build a spaceship], and we will [VP _ an orbital station ]
    (ungrammatical if what’s missing is [quickly build])

    For many speakers the contrast is clearer with do so replacement: do so can replace a verb and its object, but can’t replace an adverb and verb if this strands the object.

    (5) a. They will [VP quickly build a spaceship], and we will [VP slowly do so ]
    b. *They will [VP quickly build a spaceship], and we will [VP do so an orbital station ]
    (ungrammatical if what’s missing is [quickly build])

    As with noun phrases, we can represent the fact that the verb and its object form a constituent, to the exclusion of any adverbs, by putting them both under the V’ node.

    Tree diagram: [ VP [ AdvP [Adv' [Adv quickly ] ] ] [ V' [ V \\ build] [ NP [DP [D' [ D a ] ] ] [N' [N spaceship ] ] ] ] ]
    Figure 6.8 Tree diagram for [ quickly build a spaceship ]

    “Empty” bar levels

    As with the hypothesis that all heads project phrases, even when there are no other words in the phrase, X-bar theory assumes that all phrases contain at least one bar level, even when it is not needed to host a complement.

    So for the sentence in (6), we would have the tree in Figure 6.9, where every phrase has a bar level even though none of the phrases we’ve drawn includes a complement:

    (6) The spaceships landed.
    Tree diagram: [S [NP [DP [D' [D\\The] ] ] [N' [N\\ spaceships] ] ] [VP [V' [V\\landed] ] ] ]
    Figure 6.9 Tree diagram for The spaceships landed.

    This tree also illustrates something that’s still missing from our implementation of X-bar theory: we’ve said that every phrase has to have a head, but our sentences are currently headless. In the next section we turn to the proposal that all sentences are projected from a tense head.

    Check your understanding

    Coming soon!

    If you are following the alternative path through the chapter that interleaves core concepts with tree structures, the previous section was 6.13 From constituency to tree diagrams and the next section is 6.15 Trees: Sentences as TPs.

    Phrase Structure Rules, X-Bar Theory, and Constituency, from Sarah Harmon

    Video Script

    Anderson does an excellent job of walking you through a phrase structure tree. I'm just going to add a little bit more.

    If you want a basic set of phrase structure rules for English—and it should be noted, this is most all dialects of English, not all but most all—this is one set that you can use.

    S → NP VP

    S → CP VP

    CP → (Comp) S

    NP → (Det) (AdjP) N’ (CP) (PP) (CoordP)

    N’ → (AdjP) N’ (PP)

    N’ → N

    NP → NP’s N’

    NP → Pro

    NP → [proper name]

    VP → V’ (CP) (NP) (AdjP) (PP) (CoordP) (AdvP)

    V’ → V

    V’ → Aux V’

    AdjP → Adj (N’) (CoordP)

    AdvP → Adv (PP) (CoordP)

    PP → P NP (CoordP)

    CoordP → Coord XP

    Figure \(\PageIndex{1}\): English Phrase Structure Rules. (Copyright; Sarah Harmon)

    Catherine has a slightly modified version of this but either set will work just fine. What's important to note is that for every type of phrase, there is a head and a complement. The head is the crucial piece of that phrase, and then the complement is the supporting cast, as it were. For example, the head of a noun phrase is always going to be a noun.

    All of these little codes, as it were, are a nice shorthand for trying to decipher what role that piece has. Instead of thinking of individual morphemes and lexicons and puzzle pieces, think bigger. Think big steel beams that are being used to set up the structure of a building; that's basically what phrase structure rules are.

    As Anderson talks about, we're going to be using X-Bar Theory. It has been around for quite some time, about 40 years. It is still the prevailing method of doing basic syntactic analysis; we'll talk more about that soon enough. She does an excellent job of explaining it, it is really a great tool, not just to analyze the syntax. Morphology as well; you can use this type of structure this branching tree structure to analyze how more things are put together in a language, to create lexicon. Then you can use it to create the structure of a sentence or phrase in a given language. It has used been used for pretty much every language that is in existence; there's only a very few that it doesn't work for.

    Catherine talks quite a bit about constituency, so I’m going to leave that there, but I do want to bring up recursion. It is one of the great ways to analyze a specific phrase structure of a specific language: to look at what has allowed with respect to recursion. Recursion actually refers to that hallmark of language called duality, that we have a limited number of resources, but we can make an infinite number of statements or sentences in a given language. For example, if we scroll back to our phrase structure rules, this more or less covers every single possible sentence and phrase in English. You pretty much can blueprint English based off of these rules. Yet, these few rules explain pretty much every possible statement that you can make in English; that's recursion. It also shows up in the fact that you can have nesting of different types of phrases. For example, a noun phrase can have a propositional phrase as a complement, so ‘the cat in the house’. ‘In the house’ is modifying or describing ‘cat’. Notice that a prepositional phrase can have a noun phrase as one of its components; in fact, it has to have a noun phrase. ‘In the House’, there's your prepositional phrase, and then that noun phrase itself can get further modified by another propositional phrase: ‘the cat in the house down the hill on the river next to the forest’ and on and on and on. You can keep building quite a number of these recursive statements.

    That's possible. Is it probable? Well, no, it's not. There is a tendency to kind of keep a limit as to how many recursive elements you put in. If you think about it, that makes sense; if I start to describe where I live, ‘I live in a house on a street in the town by the river next to the forest through the gap down the gulch…’. After a minute, you stop being able to keep track of where my house is. There seems to be a limit, three to four phrases are the rough limit. That being said, could we build a structure as tall and as far as we can see? Sure. Do we do that? No, we tend to keep a limit to our height of building; we also tend to put a limit on how many recursive elements we tend to include.

    This page titled 5.7: Trees- Introducing X-bar theory is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Catherine Anderson, Bronwyn Bjorkman, Derek Denis, Julianne Doner, Margaret Grant, Nathan Sanders, and Ai Taniguchi (eCampusOntario) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.