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=== Directionality of branching === Figures 1β5 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.) {{multiple image |align=left |total_width = 700 |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 }}{{-}} 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>[Β±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 |γΈγ§γ³γ γͺγ³γ΄γ ι£γΉγ |John-ga ringo-o tabe-ta |John-NOM apple-ACC eat-PAST |'John ate an apple'}} {{multiple image |align=left |total_width = 700 |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=439β474|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.
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