In linguistics, X-bar theory is a model of phrase-structure grammar and a theory of syntactic category formation that was first proposed by Noam Chomsky in 1970 reformulating the ideas of Zellig Harris (1951), and further developed by Ray Jackendoff (1974, 1977a, 1977b), along the lines of the theory of generative grammar put forth in the 1950s by Chomsky. It attempts to capture the structure of phrasal categories with a single uniform structure called the X-bar schema, basing itself on the assumption that any phrase in natural language is an XP (X phrase) that is headed by a given syntactic category X. It played a significant role in resolving issues that phrase structure rules had, representative of which is the proliferation of grammatical rules, which is against the thesis of generative grammar.
X-bar theory was incorporated into both transformational and nontransformational theories of syntax, including government and binding theory (GB), generalized phrase structure grammar (GPSG), lexical-functional grammar (LFG), and head-driven phrase structure grammar (HPSG). Although recent work in the minimalist program has largely abandoned X-bar schemata in favor of bare phrase structure approaches, the theory's central assumptions are still valid in different forms and terms in many theories of minimalist syntax.
Background
The X-bar theory was developed to resolve the issues that phrase structure rules (PSR) under the Standard Theory had.
The PSR approach has the following four main issues. It assumes exocentric structures such as "S → NP Aux VP". This is contrary to the fact that phrases have heads in all circumstances. While the sentence John talked to the man, for example, involves the PSR of a verb phrase "VP → V (PP)", John talked to the man in person involves the PSR of "VP → V (PP) (PP)". This indicates that it is necessary to posit new PSRs every time when an undefined structure is observed in E-language, which amounts to adding an indiscriminate number of grammatical rules to Universal Grammar. This poses serious issues from the perspectives of the Plato's problem and the poverty of the stimulus. It wrongly rules in structures that are impossible in natural language such as "VP → NP A PP", because as in 1 and 2, the PSR countenances phrases that do not have endocentric structures. It fails to capture sentence ambiguities because it assumes flat, nonhierarchical structures. The X-bar theory is a theory that attempts to resolve these issues by assuming the mold or template phrasal structure of "XP".
X-bar schema
Basic principles
The "X" in the X-bar theory is equivalent to a variable in mathematics: It can be substituted by syntactic categories such as N, V, A, and P. These categories are lexemes and not phrases: The "X-bar" is a grammatical unit larger than X, thus than a lexeme, and the X-double-bar (=XP) outsizes the X(-single)-bar. X-double-bar categories are equal to phrasal categories such as NP, VP, AP, and PP.
The X-bar theory assumes that all phrasal categories have the structure in Figure 1. This structure is called the X-bar schema.
As in Figure 1, the phrasal category XP is notated by an X with a double overbar. For typewriting reasons, the bar symbol is often substituted by the prime ('), as in X'.
The X-bar theory embodies two central principles. Headedness principle: Every phrase has a head. Binarity principle: Every node branches into two different nodes. The headedness principle resolves the issues 1 and 3 above simultaneously. The binarity principle is important to projection and ambiguity, which will be explained below.
The X-bar schema consists of a head and its circumstantial components, in accordance with the headedness principle. The relevant components are as follows: Specifier: [obligatory] The node that is in a sister relation with an X' node. This is a term that refers to the syntactic position itself. Head: [obligatory] The core of a phrase, into which a lexeme fits. The head determines the form and characteristics of the phrase as a whole. Complement: [obligatory] An argument required by the head. Adjunct: [optional] A modifier for the phrase constituted by the head. The specifier, head, and complement are obligatory; hence, a phrasal category XP must contain one specifier, one head, and one complement. On the other hand, the adjunct is optional; hence, a phrasal category contains zero or more adjuncts. Accordingly, when a phrasal category XP does not have an adjunct, it forms the structure in Figure 2.
For example, the NP linguistics in the sentence John studies linguistics has the structure in Figure 3.