| A formalism in syntax developed by Ray Jackendoff and Noam Chomsky from 1970 on. It is the basis of all subsequent Chomskyan theories of syntax. It gives the same underlying structure to all phrases in a sentence, and enables generalizations to be made about structual configurations without reference to their content.
Before this generative grammar had made use of various phrase structure rules. The most basic was that a sentence consisted of a noun phrase and a verb phrase, or in traditional terms a subject and a predicate. This was symbolized by a rewrite rule S --> NP VP. Each element could be further rewritten: so a noun phrase might consist of a determiner such as the or my, an adjective, and the head noun: NP --> Det A N. A verb phrase consisted of a verb and various other elements, some optional, some depending on the nature of the verb: such as slept or saw Mary or gave Mary a book.
X-bar Theory replaces these separate and variable structures for NP, VP, and all the rest, with a single structure. Each lexical category X, which may be noun, verb, adjective, or preposition, is the head or basic word of an XP or phrase. The XP consists of the X plus its various qualifiers, and the XP is semantically of the same nature as its head X: for example, my little red book is like book, and slept fitfully all night is like slept. The XP is called a projection of its head.
The intermediate level between X and XP is notated X'. This is where the name 'X-bar' comes from: originally the level above X was denoted by one bar over the X, and the XP was denoted by two bars over it. For typographical reasons this was replaced by the prime symbol, but it is always pronounced 'bar'. The intermediate level can occur several times. For example, book is an N, the head of the phrase, red book and little red book are successive projections of N, giving two N' levels, and the maximal projection my little red book is N'' or NP. It is called maximal because in structures higher than this the component no longer behaves like an N.
Specifier, complement, and adjunct
Phrases are normally diagrammed as trees. Another key assumption of X-bar Theory is that branching is always binary, if it occurs. So the top-level XP branches into X' and something else, which is called the specifier. The lowest X' branches into X and something else, which is called the complement. This gives the following basic structure:
XP
/ \
/ \
Spec X'
/ \
/ \
X Comp
Since only binary branching is permitted, more complicated phrases are built up by multiple instances of the intermediate X'. These other elements, which are sisters of X' but not the daughter of XP, are called adjuncts or modifiers:
XP
/ \
/ \
Spec X'
/ \
/ \
X' Adjunct
/ \
/ \
X Comp
The order of elements is not important to the theory. Complements may be before or after their heads, as may specifiers. More recent work suggests there might be a universal underlying order, with surface variation derived from it. The order shown is convenient because it fits English: in my book, my is the specifier of book, and in read the book slowly, the essential element the book is the complement of the verb whereas the inessential adverb slowly is only an adjunct.
The specifier, complement, and adjunct can themselves be syntactically complex: the VP read my big red book on physics slowly has the complex NP my big red book on physics as its complement. In this NP the head book has its own complement, the prepositional phrase (PP) on physics.
Functional categories
In its earlier formulations X-bar Theory was about projections of items from the lexicon, that is real words with meanings. Some of the grammar, such as tense and agreement, was left out. Later on ways were found of bringing functional categories into the same structure. The most important are D, I, and C. These stand for determiner, inflection, and complementizer.
Determiners in English are articles like the, a, some, demonstratives like this, that, and pronominal adjectives like my, your. Any noun phrase can have at most one of these as its specifier: you can't say *the my big red book. The current theory is that while big red book is an NP, that is a projection of N, adding a determiner to it makes it a DP, not an NP: it is D that projects.
The basic subject-predicate analysis S --> NP VP was rejected from the earliest Chomskyan analysis in favour of a notation giving auxiliaries and inflection a special place: S --> NP Aux VP. This was integrated into X-bar Theory by saying that Aux, renamed first Infl then just I, was the thing that projected to give the sentence:
IP
/ \
/ \
DP I'
/ \
/ \
I VP
So a sentence can now be called an IP. Its specifier is the DP that is its subject, and its complement is the VP that is its predicate. The head I itself contains nodes for tense and agreement as well as auxiliary verbs: later versions of the theory have split I into T and Agr.
A complementizer is a word like that or if in Mary will tell John that Bill wonders if the book is useful. There are three clauses in that, and the inner ones are joined into the outer ones with a C, forming a CP above the IP. Each CP is a complement or adjunct of its preceding verb:
IP
/ \
/ \
DP I'
Mary / \
/ \
I VP
will / \
/ \
V' CP
/ \ / \
/ \ / \
V DP C IP
tell John that/ \
/ \
DP I'
Bill / \
/ \
I VP
/ \
/ \
V CP
wonders / \
/ \
C IP
if / \
/ \
--------
the book is useful
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