Editing X-bar theory

{{Short description|Linguistics theory about syntax}}
{{Redirect|X'|the sound|velar ejective fricative}}
{{Linguistics}}
In [[linguistics]], '''X-bar theory''' is a model of phrase structure and a theory of syntactic category formation<ref>{{Cite book |url=http://www.oxfordreference.com/view/10.1093/acref/9780199675128.001.0001/acref-9780199675128 |title=The Concise Oxford Dictionary of Linguistics |date=2014-01-01 |publisher=Oxford University Press |isbn=978-0-19-967512-8 |edition=3 |language=en |doi=10.1093/acref/9780199675128.001.0001}}</ref> that proposes a universal schema for how phrases are organized. It suggests that all phrases share a common underlying structure, regardless of their specific category ([[noun phrase]], [[verb phrase]], etc.). This structure, known as the '''X-bar schema''', is based on the idea that every phrase (XP, X phrase) has a [[Head (linguistics)|head]], which determines the type ([[syntactic category]]) of the phrase (X). 

The theory was first proposed by [[Noam Chomsky]] in 1970<ref name="C70">Chomsky, Noam (1970). Remarks on Nominalization. In: R. Jacobs and P. Rosenbaum (eds.) ''Reading in English Transformational Grammar'', 184–221. Waltham: Ginn.</ref> reformulating the ideas of [[Zellig Harris]] (1951<ref name="H51">{{cite book |last=Harris |first=Zellig |title=Methods in Structural Linguistics |publisher=University of Chicago Press |year=1951 |location=Chicago, IL}}</ref>), and further developed by [[Ray Jackendoff]] (1974,<ref name="J74">{{cite book |last=Jackendoff |first=Ray |title=Introduction to the X-bar Convention |publisher=Indiana University Linguistics Club |year=1974 |location=}}</ref> 1977a,<ref name="J77a">{{cite book |last=Jackendoff |first=Ray |title=X-bar-Syntax: A Study of Phrase Structure |publisher=MIT Press |year=1977a |location=Cambridge, MA}}</ref> 1977b<ref name="J77b">Jackendoff, Ray (1977b) Constraints on Phrase Structure Rules, in P. W. Culicover, T. Wasow & A. Akmajian (eds.), ''Formal Syntax'', Academic Press, New York, pp. 249–83.</ref>), along the lines of the theory of [[generative grammar]] put forth in the 1950s by Chomsky.<ref name="C55">{{Cite book |last=Chomsky |first=Noam |title=The Logical Structure of Linguistic Theory |publisher=MIT Press |year=1955 |isbn= |location=Cambridge, MA |page= |language= |id= |quote= |authorlink=}}</ref><ref name="C57">{{Cite book |last=Chomsky |first=Noam |title=Syntactic Structures |publisher=Mouton |year=1957 |isbn= |location=The Hague |page= |language= |id= |quote= |authorlink=}}</ref> It aimed to simplify and generalize the rules of grammar, addressing limitations of earlier phrase structure models. X-bar theory was an important step forward because it simplified the description of sentence structure. Earlier approaches needed many [[phrase structure rules]], which went against the idea of a simple, underlying system for language. X-bar theory offered a more elegant and economical solution, aligned with 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).<ref>{{Cite book |last=Müller |first=Stefan |url=https://langsci-press.org/catalog/book/287 |title=Grammatical theory: From transformational grammar to constraint-based approaches. |publisher=Language Science Press |year=2020 |isbn=978-3-96110-273-0 |edition=4th revised and extended |pages=75 |language=en |doi=10.5281/zenodo.3992307}}</ref> Although recent work in the [[minimalist program]] has largely abandoned X-bar schema 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]]<ref name="C65">{{Cite book |last=Chomsky|first=Noam|authorlink= |title=Aspects of the Theory of Syntax|publisher=MIT Press|location=Cambridge, MA|language= |year=1965|page= |id= |isbn= |quote= }}.</ref> had.<ref name="chom-dict-xbar">{{Cite book|author=Haraguchi|display-authors=et al.|authorlink= |translator= |title=Zouhoban Chomsky Riron Jiten|publisher=Kenkyusha|location=Tokyo|year=2016|pages=521–523|id= |isbn= |quote= |edition= Kenkyusha's Dictionary of Theoretical Linguistics Enlarged}}</ref>

The PSR approach has the following four main issues.
# It assumes [[exocentric structure]]s<ref group="FN">Phrasal structures that lack a [[head (linguistics)|head]].</ref> such as "S → NP Aux VP". This is contrary to the fact that [[phrases]] have [[head (linguistics)|heads]] in all circumstances.<ref name="chom-dict-xbar" />
# While the sentence ''John talked to the man'', for example, involves the PSR of a [[verb phrase]] "VP → V (PP)",<ref group="FN">The parentheses indicate that the [[phrasal category]] in them is optional.</ref> ''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]].<ref name="C65" />
# 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 structure]]s.<ref group="FN">Phrasal structures that include a [[head (linguistics)|head]].</ref><ref name="chom-dict-xbar" />
# It fails to capture sentence ambiguities because it assumes flat, nonhierarchical structures.<ref name="basic-GG">{{Cite book|last=Kishimoto|first=Hideki|authorlink= |title=Basic Seisei Bunpo (The Basics of Generative Grammar)|publisher=Hitsuji Shobo|location=Tokyo|language= |year=2009|page=|id= |isbn= |quote= }}</ref>
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 (mathematics)|variable]] in mathematics: It can be substituted by [[syntactic categories]] such as [[noun|N]], [[verb|V]], [[adjective|A]], and [[preposition|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 category|phrasal categories]] such as [[noun phrase|NP]], [[verb phrase|VP]], [[adjective phrase|AP]], and [[prepositional phrase|PP]].<ref name="J77a" />

The X-bar theory assumes that all [[phrasal categories]] have the structure in Figure 1.<ref name="J77a" /><ref name="C81">{{Cite book|last=Chomsky|first=Noam|authorlink= |title=Lectures on Government and Binding|publisher=MIT Press|location=Cambridge, MA|language= |year=1981|page= |id= |isbn= |quote= }}</ref> This structure is called the '''X-bar schema'''.
[[File:X-bar_schema_(basic).png|thumb|none|300px|Figure 1]]
As in Figure 1, the phrasal category XP is notated by an X with a double overbar.{{refn|group="FN"|Jackendoff (1977a)<ref name="J77a" /> assumes bar-levels up to X-triple-bar.}} For typewriting reasons, the bar symbol is often substituted by the prime ('), as in '''X''''.

{{Anchors|Headedness principle|Binarity principle}}The X-bar theory embodies two central principles.
* '''Headedness principle''': Every phrase has a head.<ref name="radford">{{Cite book|last=Radford|first=Andrew|authorlink= |translator= |year=2016|title=Analysing English Sentences: Second Edition|publisher=Cambridge University Press|location=Cambridge|pages=114–115|id= |isbn= |quote= }}</ref>
* '''Binarity principle''': Every [[node (linguistics)|node]] branches into two different nodes.<ref name="radford" />
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.

{{Anchors|Specifier|Head|Complement|Adjunct}}The X-bar schema consists of a head and its circumstantial components, in accordance with the headedness principle.<ref name="J74" /><ref name="J77a" /><ref name="J77b" /><ref name="C81" /> The relevant components are as follows:
* '''Specifier''': '''<nowiki>[</nowiki>obligatory<nowiki>]</nowiki>''' The node that is in a sister relation with an X' node.<ref>{{Cite book|editor-last1=Araki|editor-first1=Kazuo|authorlink= |translator= |year=1999|title=Eigogaku Yogo Jiten (A Dictionary of Technical Terms of English Linguistics)|publisher=Sanseido|location=Tokyo|page=587|id= |isbn= |quote= }}</ref> This is a term that refers to the syntactic position itself.
* '''[[head (linguistics)|Head]]''': '''<nowiki>[</nowiki>obligatory<nowiki>]</nowiki>''' The core of a phrase, into which a [[lexeme]] fits. The head determines the form and characteristics of the phrase as a whole.<ref><!-- name="dict"-->{{Cite book|editor-last1=Araki|editor-first1=Kazuo|authorlink= |translator= |year=1999|title=Eigogaku Yogo Jiten (A Dictionary of Technical Terms of English Linguistics)|publisher=Sanseido|location=Tokyo|page=249|id= |isbn= |quote= }}</ref>
* '''[[complement (linguistics)|Complement]]''': '''<nowiki>[</nowiki>obligatory<nowiki>]</nowiki>''' An [[argument (linguistics)|argument]] required by the head.
* '''[[adjunct (grammar)|Adjunct]]''': '''<nowiki>[</nowiki>optional<nowiki>]</nowiki>''' 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.
[[File:X-bar_schema_(wo adjunct).png|thumb|none|300px|Figure 2]]
For example, the NP ''linguistics'' in the sentence ''John studies linguistics'' has the structure in Figure 3.
[[File:The_X-bar_structure_of_the_NP_linguistics.png|thumb|none|250px|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.<ref name="C81" /> (This resolves the second issue above.) In the meantime, one needs to be wary of when such empty positions are representationally omitted as in Figure 4.
[[File:The_X-bar_structure_of_the_NP_linguistics_(simplified).png|thumb|none|130px|Figure 4]]
In illustrating syntactic structures this way, at least one X'-level node is present in any circumstance because the complement is obligatory.<ref name="chom-dict-xbar" /><ref name="C86a">{{Cite book|last=Chomsky|first=Noam|authorlink= |translator= |year=1986a|title=Barriers|publisher=MIT Press|location=Cambridge, MA|page=|id= |isbn= |quote= }}</ref>

{{Anchors|Projection|Zero-level projection|Intermediate projection|Maximal projection}}Next, the X<nowiki>''</nowiki> and X' inherit the characteristics of the head X. This trait inheritance is referred to as '''''projection'''''.<ref>{{Cite book|editor-last1=Araki|editor-first1=Kazuo| author-link= |year=1999|title=Eigogaku Yogo Jiten (A Dictionary of Technical Terms of English Linguistics)|publisher=Sanseido|location=Tokyo|page=489|id= |isbn= |quote= }}</ref>
[[File:X-bar_schema_(projection)_en.png|thumb|none|400px|Figure 5]]
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 '''X<sup>0</sup>'''.<ref>{{Cite web |url=http://primus.arts.u-szeged.hu/bese/Glossary/gloss_zero_level_projection.htm|title=Basic English Syntax with Exercises|accessdate=2021-10-22}}</ref>
# The head and the complement are combined to form an X-single-bar (<span style="text-decoration:overline">X</span>, X') node, which constitutes a semi-phrasal category (a syntactic category not as big as a phrase). This category is called '''''intermediate projection'''''.<ref name="chom-dict-xbar" />
# (An adjunct, if there is any, combines with an X' to form another X'. If there is more than one adjunct, this process is repeated.)
# An intermediate projection combines with the specifier, forming a complete phrasal category XP (X-double-bar). This category is called '''''maximal projection'''''.<ref name="chom-dict-xbar" />

It is important that all the processes except for the third are obligatory. This means that one phrasal category necessarily includes X<sup>0</sup>, <span style="text-decoration:overline">X</span>, and XP (=X<nowiki>''</nowiki>). Moreover, nodes bigger than X<sup>0</sup> (thus, <span style="text-decoration:overline">X</span> and XP nodes) are called '''[[constituent (linguistics)|constituents]]'''.<ref>{{Cite book|author=Haraguchi|display-authors=et al.|authorlink= |translator= |title=Zouhoban Chomsky Riron Jiten|publisher=Kenkyusha|location=Tokyo|year=2016|pages=125–126|id= |isbn= |quote= |edition= Kenkyusha's Dictionary of Theoretical Linguistics Enlarged}}</ref>

=== Directionality of branching ===
Figures 1–5 are based on the [[word order]] of [[English language|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.)

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|image1=The structure of "John read a long book of linguistics with a red cover"1.png
|caption1=Figure 6
|image2=The structure of "John read a long book of linguistics with a red cover"2.png
|caption2=Figure 7
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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'<sub>2</sub> and N'<sub>3</sub>: 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 approach|principles-and-parameters model of language]]''',<ref name="C86b">{{Cite book|last=Chomsky|first=Noam|authorlink= |translator= |year=1986b|title= Knowledge of Language: Its Nature, Origin and Use|publisher=Praeger|location=New York|page=|id= |isbn= |quote= }}</ref> more specifically by the '''[[head parameter]]''' (not by the X-bar schema itself). A '''[[principle (linguistics)|principle]]''' is a shared, invariable rule of grammar across languages, whereas a '''[[parameter (linguistics)|parameter]]''' is a [[typology (linguistics)|typologically]] variable aspect of the grammars.<ref name="C86b" /> One can either set their parameter with the values of "+" or "-": In the case of the head parameter, one configures the parameter of <nowiki>[±head first]</nowiki>, depending on what language they primarily speak.<ref>{{Cite book|editor-last=Araki |editor-first=Kazuo |year=1999|title=Eigogaku Yogo Jiten (A Dictionary of Technical Terms of English Linguistics)|publisher=Sanseido|location=Tokyo|page=424|id= |isbn= |quote= }}</ref> If this parameter is configured to be <nowiki>[+head first]</nowiki>, what results is '''head-initial''' languages such as English, and if it is configured to be <nowiki>[-head first]</nowiki>, what results is '''head-final''' languages such as [[Japanese language|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
|ジョンが リンゴを 食べた
|John-ga ringo-o tabe-ta
|John-NOM apple-ACC eat-PAST
|'John ate an apple'}}

{{multiple image
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|image1=The structure of "John ate an apple".png
|caption1=Figure 8
|image2=The_structure_of_"John-ga_ringo-o_tabe-ta".png
|caption2=Figure 9
}}{{-}}

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)<ref>{{cite journal|last1=Saito|first1=Mamoru|last2=Naoki|first2=Fukui|year=1998|title=Order in Phrase Structure and Movement|url=|journal=Linguistic Inquiry|volume=29|issue=3|pages=439–474|doi=10.1162/002438998553815|s2cid=57572491 |accessdate=}}</ref> 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 ==
=== Structure of S ===
Under the PSR, the structure of '''S''' (sentence) is illustrated as follows.<ref name="C55" /><ref name="C57" /><ref name="C75">{{Cite book|last=Chomsky|first=Noam|authorlink= |title=The Logical Structure of Linguistic Theory|publisher=Plenum Press|location=New York|language= |year=1981|page= |id= |isbn= |quote= }}</ref>
* S → NP (Aux) VP
However, this structure violates the headedness principle because it has an exocentric, headless structure, and would also violate the binarity principle if an [[Auxiliary verb|Aux]] (auxiliary) occurs, because the S node will then be ternary-branching. Given these, Chomsky (1981)<ref name="C81" /> proposed that S is an '''InflP''' headed by the functional category '''[[inflection|Infl]]'''(ection), and later in Chomsky (1986a),<ref name="C86a" /> this category was relabelled as '''I''' (hence constitutes an '''IP'''), following the notational convention that phrasal categories are represented in the form of XP, with two letters.{{refn|group="FN"|The functional category I was later replaced by '''T'''(ense) and '''Agr'''(eement) along the proposal by Pollock (1989).<ref>{{Cite journal|last=Pollock|first=Jean-Yves|date=1989|title=Verb Movement, Universal Grammar, and the Structure of IP|journal=Linguistic Inquiry|volume=20|issue=3|pages=365–424}}</ref> The functional category Agr, however, was rejected by Chomsky (1995)<ref name="C95b">{{cite book|last=Chomsky|first=Noam|title=The Minimalist Program |date=1995 |publisher=MIT Press |location=Cambridge MA}}</ref> because it presumably made no contributions at LF. For this reason, clauses are generally assumed to be '''TP'''s headed by the functional category '''T''' in contemporary linguistic theory.}} The category I includes auxiliary verbs such as ''will'' and ''can'', clitics such as ''-s'' of the third person singular present and ''-ed'' of the past tense. This is consistent with the headedness principle, which requires that a phrase have a head, because a sentence (or a clause) necessarily involves an element that determines the inflection of a verb.

Assuming that S constitutes an IP, the structure of the sentence ''John studies linguistics at the university'', for example, can be illustrated as in Figure 10.{{refn|group="FN"|{{Anchors|Affix hopping|Affix movement}}In the structure in Figure 10, the [[linear order (linguistics)|linear order]] of the whole sentence is derived by '''affix hopping''' (also known as '''affix movement'''). Affix hopping is an operation that is applied at [[phonological form]] (PF) after syntactic formation, and in this case, it serves to move the "sound" of the inflectional suffix /-s/ and adjoin it onto the verb.<ref>{{Cite book|editor-last1=Araki|editor-first1=Kazuo|authorlink= |translator= |year=1999|title=Eigogaku Yogo Jiten (A Dictionary of Technical Terms of English Linguistics)|publisher=Sanseido|location=Tokyo|page=16|id= |isbn= |quote= }}</ref> Chomsky (1981)<ref name="C81" /> calls this kind of tense affix movement ''Rule R''.}}
[[File:The_X-bar_structure_of_"John_studies_linguistics_at_the_university".png|thumb|none|600px|Figure 10]]
As is obvious, the IP hypothesis makes it possible to regard the grammatical unit of sentence as a phrasal category. It is also important that the configuration in Figure 10 is fully compatible with the central assumptions of the X-bar theory, namely the headedness principle and the binarity principle.

=== Structure of S' ===
Words that introduce [[subordinate clause|subordinate]] or [[complement clause]]s are called '''[[complementizer]]s''',<ref name="radford-C">{{Cite book|last=Radford|first=Andrew|authorlink= |translator= |year=2016|title=Analysing English Sentences: Second Edition|publisher=Cambridge University Press|location=Cambridge|pages=86–99|id= |isbn= |quote= }}</ref> and representative of them are ''that'', ''if'', and ''for.''{{refn|group="FN"|Sometimes, ''whether'' is also regarded as a complementizer, but many researchers such as Nakajima (1996)<ref>{{Cite journal|last=Nakajima|first=Heizo|date=1996|title=Complementizer Selection|journal=The Linguistic Review|volume=13|issue=2|pages=143–164|doi=10.1515/tlir.1996.13.2.143 |s2cid=201091227 }}</ref> analyze that ''whether'' does not occur in the head position of CP, but in the specifier position of CP ('''Spec-CP'''), just as [[wh-words]] do. This amounts to saying that ''whether'' is not a C<sup>0</sup>: It is subject to debate as to which syntactic category it belongs to.}} Under the PSR, complement clauses were assumed to constitute the category '''S''''.<ref name="B70">{{Cite journal|last=Bresnan|first=Joan|date=1970|title=On Complementizers: Toward a Syntactic Theory of Complement Types|journal=Foundations of Language|volume=6|issue=|pages=297–321}}</ref><ref name="B72">Bresnan, Joan (1972) ''Theory of Complementation in English Syntax'', Doctoral dissertation, MIT.</ref><ref name="B79">{{Cite book|last=Bresnan|first=Joan|authorlink= |translator= |year=1979|title=Theory of Complementation in English Syntax|publisher=Garland|location=New York|page=|id= |isbn= |quote= }}</ref>
* S' → COMP S
Chomsky (1986a)<ref name="C86a" /> proposed that this category is in fact a '''CP''' headed by the functional category '''C'''.<ref name="radford-C" /> The sentence ''I think that John is honest'', for example, then has the following structure.
[[File:The_structure_of_"I_think_that_John_is_honest".png|thumb|none|700px|Figure 11]]
Moreover, Chomsky (1986a)<ref name="C86a" /> assumes that the landing site of [[wh-movement]] is the specifier position of CP ('''Spec-CP'''). Accordingly, the [[Wh question|wh-question]] ''What did John eat?'', for example, is derived as in Figure 12.{{refn|group="FN"|[[Wh-movement]] is subject to Chomsky's (1973)<ref>Chomsky, Noam (1973). Conditions on Transformations. In: Stephen R. Anderson and Paul Kiparsky (eds.) ''A Festschrift for Morris Halle'', 232–286. New York: Holt, Rinehart, and Winston.</ref> '''[[subjacency condition]]''', and is applied in a '''successive cyclic''' manner, thus via every Spec-CP.}}
[[File:The_structure_of_"What_did_John_eat?".png|thumb|none|450px|Figure 12]]
In this derivation, the I-to-C movement is an instance of '''[[subject-auxiliary inversion]]''' (SAI), or more generally, '''[[head movement]]'''.{{refn|group="FN"|See Baker (1988)<ref>Baker, Mark C. (1988). ''Incorporation: A Theory of Grammatical Function Changing''. Chicago: University of Chicago Press.</ref> for details.}}

=== Other phrasal structures ===
* '''[[VP-internal subject hypothesis]]''': A hypothesis on the inner structure of VP proposed by researchers such as Fukui and Speas (1986)<ref>Fukui, Naoki and Speas, Margaret J. (1986) Specifiers and Projection. ''MIT Working Papers in Linguistics'' '''8''': 128–172.</ref> and Kitagawa (1986).<ref>Kitagawa, Yoshihisa (1986). ''Subjects in Japanese and English'', Unpublished doctoral dissertation, University of Massachusetts. Reprinted in Kitagawa (1994), Routledge.</ref> It assumes that the sentential subject is base-generated in Spec-VP, not in Spec-IP.
* '''DP Hypothesis''': A hypothesis proposed by Abney (1987),<ref>Abney, Steven P. (1987). ''The English Noun Phrase in Its Sentential Aspect''. Doctoral dissertation, MIT.</ref> according to whom noun phrases are not NPs but DPs headed by the functional category D.
* '''VP shell''': An analysis put forth by Larson (1988),<ref>Larson, Richard K. (1988). On the Double Object Construction. ''Linguistic Inquiry'' '''19''' (3): 335–391.</ref> which assumes two-layered structures of VP. Later in Chomsky (1995a,<ref name="C95a">{{Cite book |last=Chomsky |first=Noam |title=Evolution and revolution in linguistic theory |date=1995 |publisher=Georgetown University Press |isbn=978-0-87840-248-9 |editor-last=Campos |editor-first=Héctor |location=Washington, D.C. |pages=51–109 |chapter=Bare Phrase Structure |editor-last2=Kempchinsky, Paula Marie}}</ref> 1995b<ref name="C95b" />), the higher VP was replaced by ''v''P headed by the functional category ''v'' (little/small v, traditionally written in italics).
* '''PredP Hypothesis''': A hypothesis proposed by Bowers (1993,<ref>{{Cite journal|last=Bowers|first=John|date=1993|title=The Syntax of Predication|journal=Linguistic Inquiry|volume=24|issue=|pages=591–656}}</ref> 2001<ref>Bowers, John (2001). Predication. In: Mark Baltin and Chris Collins (eds.), ''The Handbook of Contemporary Syntactic Theory'', 299–333, Blackwell.</ref>), according to whom [[small clause]]s<ref>Stowell, Timothy (1981). ''Origins of Phrase Structure''. Doctoral dissertation, MIT.</ref> are PredPs headed by the functional category Pred.
* '''[[Bare Phrase Structure]]''' (BPS): A replacement of the X-bar theory put forth by Chomsky (1995a,<ref name="C95a" /> 1995b<ref name="C95b" />). It dispenses with a "template" structure like the X-bar schema, and yields syntactic structures by (iterative applications of) an operation called [[Merge (linguistics)|Merge]], which serves to connect two syntactic objects such as words and phrases into one. Some radical versions of it even reject syntactic category labels such as V and A. See also [[Minimalist Program]].


== Hierarchical structure ==
The PSR has the shortcoming of being incapable of capturing sentence ambiguities.
* I saw a man with binoculars.<ref name="binos">{{Cite web |author= |url=https://www.bu.edu/linguistics/ug/course/lx522-f05/lx522/archives/16.html|title=Syntax I|website= |publisher= |date= |accessdate=2021-10-23}}</ref>
This sentence is ambiguous between the reading ''I saw a man, using binoculars'', in which ''with binoculars'' modifies the VP, and the reading ''I saw a man who had binoculars'', in which the PP modifies the NP.<ref name="binos" /> Under the PSR model, the sentence above is subject to the following two parsing rules.
* S → NP VP
* VP → V NP PP
The sentence's structure under these PSRs would be as in Figure 13.

[[File:The_PSR_structure_of_"I_saw_a_man_with_binoculars".png|thumb|none|500px|Figure 13]]

It is obvious that this structure fails to capture the NP modification reading because [<sub>PP</sub> with binoculars] modifies the VP no matter how one tries to illustrate the structure. The X-bar theory, however, successfully captures the ambiguity as demonstrated in the configurations in Figure 14 and 15 below, because it assumes hierarchical structures in accordance with the binarity principle.

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|align=left
|total_width = 800
|image1=The_X-bar_structure_of_"I_saw_a_man_with_binoculars"1.png
|caption1=Figure14
|image2=The_X-bar_structure_of_"I_saw_a_man_with_binoculars"2-revised.png
|caption2=Figure15
}}{{-}}

Thus, the X-bar theory resolves the fourth issue mentioned in {{Section link||Background}} as well. There is always a unilateral relation from syntax to semantics (never from semantics to syntax) in any version of [[generative grammar]] because syntactic computation starts from the [[lexicon]], then continues into the syntax, then into [[Logical form (linguistics)|Logical Form]] (LF) at which meanings are computed. This is so under any of [[Standard Theory]] (Chomsky, 1965<ref name="C65" />), [[Extended standard theory|Extended Standard Theory]] (Chomsky, 1972<ref name="C72">{{Cite book |last=Chomsky|first=Noam|authorlink= |title=Studies on Semantics in Generative Grammar|publisher=Mouton|location=The Hague|language= |year=1972|page= |id= |isbn= |quote= }}</ref>), and [[Revised extended standard theory|Revised Extended Standard Theory]] (Chomsky, 1981<ref name="C81" />).

== Footnotes ==
{{Reflist|group="FN"|2}}

== References ==
{{Reflist|2}}

== See also ==
{{colbegin|colwidth=15em}}
* [[Antisymmetry]]
* [[Linguistics]]
* [[Natural language]]
* [[Syntax]]
* [[Constituent (linguistics)]]
* [[Parse tree]]
* [[Head (linguistics)]]
* [[Complement (linguistics)]]
* [[Phrase]]
* [[Syntactic category]]
* [[Lexical category]]
* [[Functional category]]
* [[Part of speech]]
* [[Node (linguistics)]]
* [[Generative grammar]]
* [[Universal Grammar]]
* [[Plato's problem]]
* [[Poverty of the stimulus]]
* [[Transformational grammar]]
* [[Phrase structure grammar]]
* [[Phrase structure rule]]
* [[Standard Theory]]
* [[Extended Standard Theory]]
* [[Revised Extended Standard Theory]]
* [[Government and binding theory]]
* [[C-command]]
* [[Principles-and-parameters approach]]
* [[Minimalist Program]]
{{colend}}

{{DEFAULTSORT:X-Bar Theory}}
[[Category:Linguistics]]
[[Category:Generative syntax]]
[[Category:Grammar]]
[[Category:Syntactic relationships]]
[[Category:Syntactic categories]]
[[Category:Phrases]]
[[Category:Linguistic units]]
[[Category:Linguistics terminology]]
[[Category:Syntactic theories]]