X-bar theory

The X-bar theory was first proposed by Noam Chomsky (1970). It postulates that all human languages share certain structural similarities, including the same underlying syntactic structure, which is known as the "X-bar". The Default Grammar is based in a modified version of the X-bar approach.

X-bar

The X-bar abstract configuration is depicted in the diagram below:

    XP
   / \
spec  XB
     / \
    XB  adjt
   / \
  X   comp
  |
head

In the above:

• X is the head, the nucleus or the source of the whole syntactic structure, which is actually derived (or projected) out of it. The letter X is used to signify an arbitrary lexical category (part of speech). When analyzing a specific utterance, specific categories are assigned. Thus, the X may become an N for noun, a V for verb, an J for adjective, or a P for preposition.
• comp (i.e., complement) is an internal argument, i.e., a word, phrase or clause which is necessary to the head to complete its meaning (e.g., objects of transitive verbs)
• adjt (i.e., adjunct) is a word, phrase or clause which modifies the head but which is not syntactically required by it (adjuncts are expected to be extranuclear, i.e., removing an adjunct would leave a grammatically well-formed sentence)
• spec (i.e., specifier) is an external argument, i.e., a word, phrase or clause which qualifies (determines) the head
• XB (X-bar) is the general name for any of the intermediate projections derived from X
• XP (X-bar-bar, X-double-bar, X-phrase) is the maximal projection of X.

Constituents

The head, the complement, the specifier and the adjunct are said to be the constituents of the syntactic representation and define the four general universal syntactic roles.

Heads

In the X-bar diagram depicted above, the letter X is used to signify an arbitrary category. Thus, the X may become an N for noun, a V for verb, and so on. In the UNLarium framework, there are eight different types of heads:

• N = nouns and nominals: personal pronouns, demonstrative pronouns, nominalizations, etc
• V = verbs
• J = adjectives
• A = adverbs
• P = prepositions
• D = determiners: articles, demonstrative determiners, possessive determiners, quantifiers
• I = auxiliary verbs
• C = conjunctions

The heads define the nature of the phrase structures, thus:

• N projects a Noun Phrase (NP)
• V projects a Verbal Phrase (VP)
• J projects an Adjective Phrase (JP)
• A projects an Adverbial Phrase (AP)
• P projects a Prepositional Phrase (PP)
• D projects a Determiner Phrase (DP)
• I projects an Inflectional Phrase (IP)
• C projects a Complementizer Phrase (CP)

Noun Phrase	Verbal Phrase	Adjective Phrase	Adverbial Phrase	Prepositional Phrase	Determiner Phrase	Inflectional Phrase	Complementizer Phrase
NP / \ spec NB / \ NB adjunct / \ N comp | noun	VP / \ spec VB / \ VB adjunct / \ V comp | verb	JP / \ spec JB / \ JB adjunct / \ J comp | adjective	AP / \ spec AB / \ AB adjunct / \ A comp | adverb	PP / \ spec PB / \ PB adjunct / \ P comp | preposition	DP / \ spec DB / \ DB adjunct / \ D comp | determiner	IP / \ spec IB / \ IB adjunct / \ I comp | auxiliary verb	CP / \ spec CB / \ CB adjunct / \ C comp | conjunction

Specifiers

Specifiers are used to narrow the meaning intended by the head. They include:

• articles: the (book), a (book), etc.
• possessive determiners: my (book), your (book), etc.
• demonstrative determiners: this (book), that (book), etc.
• quantifiers: no (answer), every (hour), etc.
• intensifiers (emphasizers, amplifiers, downtoners): very (expensive), quite (well), nearly (under), kind of (like), etc.

Complements

Complements are used to complete the meaning intended by the head. They may be:

• direct objects: (do) something, (give) something
• indirect objects: (laugh at) something, (give to) someone
• complement of deverbals (i.e., nouns deriving from verbs): (construction of) the city, (arrival of) Peter
• complement of adjectives: (loyal) to the queen, (interested) in Chemistry
• complement of adverbs: (contrarily) to popular belief, (independently) from her
• complement of prepositions: (under) the table, (after) today
• complement of conjunctions: (and) Peter, (I don't know if) he'll come

Adjuncts

Adjuncts are used to modify the meaning intended by the head:

• adjectives: beautiful (table)
• adverbs: (speak) slowly
• prepositional phrases: (table) of wood

Examples

NP	VP	JP	PP
NP / \ / \ / \ / NB / / \ spec head comp | | | D N PP | | | the construction of Babel	VP | VB / \ / \ / \ VB \ / \ \ head comp adjt | | | V N A | | | (he) bought something yesterday	JP / \ / \ / \ / JB / / \ spec head comp | | | A J PP | | | (I'm) really interested in Chemistry	PP | PB / \ head N | | without notice

Phrases

Specifiers, complements and adjuncts are themselves complex syntactic structures (XPs) which are combined to form the sentence structure:

PHRASE	STRUCTURE
	XP
	SPEC	XB
		XB		ADJT
		HEAD	COMP
NP	DP	N	PP	JP,PP
VP	NP	V	NP,PP	PP,JP,AP
JP	AP	J	PP	AP,PP
AP	AP	A	PP	PP,AP
PP	AP	P	NP,JP,VP	AP
DP	AP	D		AP
IP	NP	I	VP	AP
CP	AP	C	IP	AP

Examples

construction	the construction	the fateful construction	the fateful construction of Babel
NP | NB | N | construction	NP / \ spec NB | | DP N | | DB construction | D | the	NP / \ spec NB | / \ DP adjt N | | | DB JP construction | | D JB | | the J | fateful	NP / \ spec NB | / \ DP adjt NB | | / \ DB JP N comp | | | | D JB construction PP | | | the J PB | / \ fateful P comp | | of NP | NB | N | Babel

Properties

Branching is binary

A key assumption of X-bar theory is that branching is always binary, if it occurs. This means that specifiers, complements and adjuncts are optional and that there can be as many XBs as necessary:

XP | XB | head

XP / \ spec XB | head

XP | XB / \ head comp

XP | XB / \ head adjt

XP / \ spec XB / \ head adjt

XP / \ spec XB / \ XB comp / \ X comp | head

XP / \ spec XB / \ XB adjt / \ XB comp / \ X comp | head

etc.

Order is parametrized

The order of the constituents (specifiers, complements and adjuncts) is subject to language specific parametrization and may vary:

right complement	left complement	right adjunct	left adjunct
XP | XB / \ head comp	XP | XB / \ comp head	XP | XB / \ head adjt	XP | XB / \ adjt head	etc.

Conventions

The following conventions have been adopted in the Default Grammar. They do not correspond to the current assumptions of the X-bar theory, and derive rather from extralinguistic issues (such as machine-tractability).

Coordination

In the original X-bar approach, branching is always binary. In the Default Grammar, this is also true, except for coordination, where branching is ternary. In any case, the coordinated constituents always project a structure of the same category (two coordinate NP's project a NP, two coordinated NB's project a NB, and so on). In case of a coordination of more than two constituents, the coordination must be represented in separate steps (i.e., branching cannot be bigger than 3).

Deep and Surface Structures

The Default Grammar differentiates between the surface syntactic structure and the deep syntactic structure. The former preserves the order of the words in the sentence; the latter preserves the dependency relations. The deep structure is converted into the surface structure, and vice-versa, through the movement of the constituents. This entails different configurations for the same sentence, as indicated below.

General configuration

The Default Grammar adopts the following general configuration, where CP is the topmost category, IP is the complement of CP, and VP is the complement of IP.

CP

CP is the maximal projection of a conjunction. It is also used to represent topicalization (i.e., movement of a constituent out of its original position to the beginning of the sentence).
Differently from the current X-bar approach, the Default Grammar considers a clause to be an instance of CP (instead of DP). However, CP is represented only in two cases:

• When there is a subordinating conjunction, which will be the head of CP; and
• In the surface structure, when there is any topicalization. In this case, the topicalized constituent is represented at the position of adjunct of CP (even if the head of CP is empty).

CP is not represented when there is no subordinating conjunction or topicalized element.

IP

IP is the maximal projection of an auxiliary verb. Differently from the current X-bar approach, only auxiliary verbs may occupy the position of the head of IP. IP is represented in the following cases:

• When the sentence contains an auxiliary verb, which will be the head of IP; and
• When there is a CP and the sentence is finite (i.e., it is inflected in tense, aspect or mood).

IP is not represented when there is no CP or auxiliary verb. The subject of a sentence is represented at the position of the spec of IP whenever the sentence contains an auxiliary verb. If this is not the case, and the subject is not topicalized, the subject is always represented at the position of the spec of VP.

VP

VP is the maximal projection of a main verb or a copula (but not of an auxiliary verb). It may contain one single specifier (the subject of the clause) and as many adjuncts and complements as necessary. The position of the spec of VP is occupied only if there is no auxiliary verb (in this case the subject is represented as the spec of IP) or when the subject is not topicalized (in this case it is represented as the adjunct of CP). There is no structural difference between complements (either direct or indirect) or adjuncts. They are always represented as branches of the intermediate projection. Predicates are represented as complements of copula (linking) verbs.

NP

NP is the maximal projection of a noun. It may contain one single specifier (DP), and as many adjuncts and complements as necessary.

JP

JP is the maximal projection of an adjective. It may contain one single specifier (AP), and as many adjuncts and complements as necessary.

AP

AP is the maximal projection of an adverb. It may contain one single specifier (other AP), and as many adjuncts and complements as necessary.

PP

PP is the maximal projection of a preposition. It may contain one single specifier (AP), and as many adjuncts and complements as necessary.

DP

DP is the maximal projection of a determiner. It may contain one single specifier (other DP) and adjuncts. A DP may not contain complements.

Further reading

• Wikipedia