Course:LING300/X-bar Theory

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X-bar Theory: A Completely General Theory of Phrase Structure

Principles of X-bar Theory

X-bar Theory is an outgrowth of the phrase structure grammars, and was first introduced in the 1970s. It is an attempt to provide a completely general theory of phrase structure for all human languages. X-bar Theory is built on four guiding principles: (i) headedness; (ii) complementation; (iii) specification; (iv) adjunction.

All phrases have a head

This property of phrase structure — that all phrases (XPs) have a unique head (X) — can be collapsed into a single general rule

X' → … X …
where "X" is variable that ranges over the set of categories, e.g. X = V, N, A, P, T, C, D, Asp, Num, …

For example the head of VP is V; the head of NP is N; the head of PP is P, the head of AP is A, and so on.

VP → … V …
NP → … N …
PP → … P …
AP → … A …

Recognizing that headedness (also called "endocentricity") is a property of all phrase structure rules was the first step to developing what is now known as X-bar Theory.

All heads can introduce a complement

This property of phrase structure — that all heads (X) have a complement (YP) can also be collapsed into a single general rule:

where YP is DP, PP, or CP

Once the central role of the "head of a phrase" is recognized, the next step is to recognize that all head can introduce a complement. Complements to V and P are DP or CP; complements to N and A are PPs. As for Functional categories (e.g. C, T, D, Num) , they select for a unique complement: C selects for a TP complement, T selects for a VP complement, D selects for a NumP complement, Num selects for an NP complement.

VP → … V {DP, CP}
NP → … N {PP, CP}
PP → … P {DP, CP}
AP → … A {PP, CP}
CP → … C TP
TP → … T VP
DP → … D NumP
NumP → … Num NP

All phrases can introduce a specifier

[add text]


Although there was general agreement from the outset that all phrases had a head, and that every head could introduce a complement, it took longer for syntacticians to come to some agreement about the specifier position. Earlier versions of X-bar theory of the 1970s and 1980s use the specifier position for determiners (which in these earlier analyses were analyzed as occupying Spec,NP) and for auxiliaries (which were analyzed as occupying Spec,VP). However, other considerations — on the one hand the recognition that closed-class items were heads in their own right, and on the other hand the development of more fine-grained diagnostics for argument positions — lead to a re-conceptualization of the specifier position as the host for "subjects". Once again, this property of phrase structure — that all phrases have a specifier (ZP) can be collapsed into a single general rule:

All phrases can host an adjunct

Again, there is a single general adjunction rule:


Modifiers are adjoined to the XP that they are construed with: WP is an adjunct if it is sister to and immediately dominated by XP.

The X-bar Theory template

Taken together, these four structural principles define the three rewrite rules of X-bar Theory:


These rewrite rules are often presented as a structural template:

Caption: X-bar Theory Template

Consequences of X-bar Theory

Silent heads

Cross-categorical symmetries

Subjects across categories

Word order

Strictly speaking, the "rules" of X-bar Theory specify only immediate dominance. This means that for one of the three rules, the elements can be ordered in one of two ways;

Head-initial versus head-final order
Head-Complement order (= head-initial order)
X' → X YP
Complement-Head order (= head-final order)
X' → YP X
Specifier-initial versus specifier-final order
Specifier-initial order
XP → ZP X'
Specifier-final order
XP → X' ZP
Adjunct-initial versus adjunct-final order
Adjunct-initial order
Adjunct-final order

The Model of Grammar

The morphological component

Caption: The morphological component

The syntactic component

File:Syntactic Component 08Sept2014.pdf

Comparing the morphological and syntactic components

File:Morpho Syn Components 08Sept2014.pdf

What they share How they differ
Morphology Syntax
Atoms morphemes and words words
Recursive Merge Merge (X, Y) Merge (X, Y, Z)
[Y X Y] [XP WP [X' X YP ZP ] ]
Labeled trees Right-hand head rule X-bar Theory
Selection under sisterhood within local projection

Connecting X-bar Theory to lexical entries

Core concepts of X-bar Theory

of syntax, of morphology
morpheme (bound, free)
part-of-speech, distribution class, word-class, open class, closed class, verb, adjective, noun, preposition, complementizer, subcategory, phrasal category, lexical category, functional category
morphological distribution, syntactic distribution, complementary distribution
constituency test
lexical property
phonological property, semantic property, syntactic property;
lexical entry, unpredictable information)
thematic relation
Cause, Agent, Experiencer, Location, Goal, Beneficiary, Possessor Posessee/Possessed, Theme)
grammatical function
subject, object);
c-selection, s-selection
projection, projection principle
labeled tree, derived tree, sisterhood, mother node, daughter node, binary branching, n-ary branching
X-bar Theory
head, specifier, complement, adjunct
silent head, Right-hand head rule (RHHR)
small clause
cross-linguistic variation
architecture, morphological component, syntactic component

Practice exercises for X-bar Theory

The following exercises allow you to check whether you have mastered the concepts of X-bar Theory. (Before attempting to do this practice set, review Chapter 6 of Sportiche, Koopman & Stabler.)


This exercise asks you to draw trees of simple sentences using the phrase structure principles of X-bar Theory.

Assume the following lexicon
  • Verb: { be, buy, leave, live, put, study, raise, read, see, think, visit, write }
  • Noun: { brother, book, books, cattle, client, contract, corner, cousins, daughter, dealership, friend, girl, hair, holidays, memo, sheep, sportscar, students, woman }
  • DP: { her, Italy, Lucy, Maya, New York, Russian, Vancouver }
  • Adjective: { heavy, new, older, proud, red, tall, used }
  • Preposition: { during, from, in, of, on, to, with }
  • Determiner: { ∅, a, that, this, the, these, ’s }
  • Complementizer: { that }
  • Tense: { can, could, must, might, should, will }

Using X-bar Theory, draw the trees for the following sentences:

    (1) The new students will study Russian.
    (2) This client might buy that red sportscar.
    (3) Lucy’s older brother will raise cattle.
    (4) The girl with the red hair should put the heavy book on the table in the corner.
    (5) Lucy will write her memo quickly.
    (6) Lucy will write to her cousins in Italy. (Note: cousins are in Italy)
    (7) Lucy will visit her cousins in Italy. (Note: visiting is in Italy)
    (8) Lucy will say that Maya will visit tomorrow.
    (9) Lucy could buy a used sportscar from Italy from a dealership in Vancouver.
    (10) Lucy will be amazingly tall.
    (11) Lucy might read these books during the holidays.
    (12) Maya must think that Lucy will leave.
    (13) Lucy can see the incredibly tall woman.
    (14) Lucy will live in New York with a friend.
    (15) Lucy will read the contract very carefully.
    (16) Lucy will be proud of her daughter.

Lexical entries

Before completing these practice exercises, review §6.8.2 of Sportiche, Koopman and Stabler.

For each of the following words, specify their lexical entry by indicating their category and their selectional properties. The first one is done for you by way of example.

    (1) laugh
    (2) live
    (3) leave
    (4) read
    (5) write
    (6) put
    (7) buy
    (8) think
    (9) know
    (10) see
    (11) mess
    (12) friend
    (13) happy
    (14) proud
    (15) tall
    (16) in
    (17) at
Sample answer for (1)
Laugh is an optionally transitive verb and that introduces an obligatory DP Agent, and an optional PP Goal. This is indicated in the lexical entry by listing the category of laugh (V) and its argument structure.
  • Argumentation: Example (1a) establishes that laugh can introduce a single DP argument with the semantic role Agent. Put more succinctly: laugh selects for a DP Agent. This is further confirmed by (1b), which is a small clause environment where laugh appears without inflection. (In traditional English grammar, such verbs are called bare infinitives.) And (1c) shows that laugh can't introduce a second DP argument. Finally, (1d) shows that laugh can introduce a PP Goal as its second argument. Comparison of (1a) and (1d) establishes that the PP argument is optional: it can be there, but it need not be there.
    (1)	laugh: V, < DPAGENT, (PPGOAL) >
          a. Maya laughed.
          b. I saw [Maya laugh].
          c. *Maya laughed Lucy.
          d. Maya laughed at Lucy.
  • PUT IN BOX Notation: In the lexical entry, optionality is indicated by putting parentheses "(…)" around the argument that is optional.
  • PUT IN BOX Notation: The argument structure is given in angle brackets "<…>"; sometimes it's given in square brackets "[…]" or parentheses "(…)". These are all equivalent notations. Note that SKS don't use brackets at all when they specify the argument structure of a lexical item. In this course, we'll use the angle bracket notation.