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. 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. 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. It is important that even if there are no candidates that can fit into the specifier and complement positions, these positions are syntactically present, and thus they are merely empty and unoccupied. (This is a natural consequence of the binarity principle.) This means that all phrasal categories have fundamentally uniform structures under the X-bar schema, which makes it unnecessary to assume that different phrases have different structures, unlike when one adopts the PSR. Next, the X'' and X' inherit the characteristics of the head X. This trait inheritance is referred to as
projection. Figure 5 suggests that syntactic structures are derived in a bottom-up fashion under the X-bar theory. More specifically, the structures are derived via the following processes. • A lexeme is fitted into the head. Heads are sometimes called
zero-level projections because they are X-zero-bar-level categories, notated as
X0. • The head and the complement are combined to form an X-single-bar (X, X') node, which constitutes a semi-phrasal category (a syntactic category not as big as a phrase). This category is called
intermediate projection.
Directionality of branching Figures 1–5 are based on the
word order of
English, but the X-bar schema does not specify the directionality of branching because the binarity principle does not have a rule on it. For example,
John read a long book of linguistics with a red cover, which involves two adjuncts, may have either of the structures in Figure 6 or Figure 7. (The figures follow the convention of omitting the inner structures of certain phrasal categories with triangles.) The structure in Figure 6 yields the meaning
the book of linguistics with a red cover is long, and the one in Figure 7
the long book of linguistics is with a red cover (see also #Hierarchical structure). What is important is the directionality of the nodes N'2 and N'3: One is left-branching, while the other is right-branching. Accordingly, the X-bar theory, more specifically the binarity principle, does not impose a restriction on how a node branches. When it comes to the head and the complement, their relative order is determined based on the
principles-and-parameters model of language, more specifically by the
head parameter (not by the X-bar schema itself). A
principle is a shared, invariable rule of grammar across languages, whereas a
parameter is a
typologically variable aspect of the grammars. If this parameter is configured to be [+head first], what results is
head-initial languages such as English, and if it is configured to be [-head first], what results is
head-final languages such as
Japanese. For example, the English sentence
John ate an apple and its corresponding Japanese sentence have the structures in Figure 8 and Figure 9, respectively. {{fs interlinear|lang=ja|indent=2 Finally the directionality of the specifier node is in essence unspecified as well, although this is subject to debate: Some argue that the relevant node is necessarily left-branching across languages, the idea of which is (partially) motivated by the fact that both English and Japanese have subjects on the left of a VP, whereas others such as Saito and Fukui (1998) argue that the directionality of the node is not fixed and needs to be externally determined, for example by the head parameter. == Structure of sentence ==