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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

X-Bar theory is bogus

Noam Chomsky proposed the X-bar theory to explain describe a universal grammatical structure, common to all language.  An admirable objective.  The problem is, it's batshit crazy.  If you haven't heard already go and read the node above, I can wait.

Right, so the idea is that every part of speech is a "phrase", not just a word.  Some are almost always single words (called a head) such as noun phrases. "dog" is a valid example.  However all of them can be extended.  That is, in every situation where you need a noun phrase you can use a longer noun phrase.

Some phrases have a minimum length because they require other sub-phrases.  This is true for many verbs, specifically intransitive verbs.

"The quick brown fox jumps over a lazy dog" has two noun phrases ("the quick brown fox" and "a lazy dog"), some adjectival phrases ("quick brown", "quick", "brown", "lazy"), a prepositional phrase ("over a lazy dog") and a verb phrase (the whole damn thing).

Already this is starting to look like hard work, but that's fine, we're just being rigorous.  We can represent this sentence in the syntax tree that defines X-bar:

                          VP                                      
                         /  \                                     
                        /    \                                    
                       /      \                                   
                      /        \                                  
                     /          \                                 
                    /            V'                               
                   /            /  \                              
                  /            /    \                             
                 /            V0     PP                           
                /             |     /  \                          
               /              |    /    \                         
              /             jumps {}     P'                       
             NP                         /  \                      
            /  \                       /    \                     
           /    \                    P0      P'                   
         The     N'                   |     /  \                  
                /  \                 over  /    \                 
               /    \                     {}     NP               
              AP     \                          /  \              
             /  \     \                        /    \             
            /    \     \                     the     N'           
           {}     A'    \                           /  \          
                 /  \    \                         /    \         
                /    \    \                       AP     N0       
               AP     \    \                     /  \      \      
              /  \     \    \                   /    \      \     
             /    \     \    \                 {}     A'     dog  
            {}    A'     \    \                      /  \         
                   |      \    \                    /    \        
                   |       \    \                  {}     A0       
                  A0       A0   N0                         |      
                   |        |    |                        lazy    
                 quick   brown   |                                
                                fox                               
  
  
  
  
  
  
  

There are lots of empty levels in this tree, but that's fine really, because we're allowing for all the possible ways you can slot words together, not just in English but in every conceivable language. There are plenty of weird things that have to be possible.

Wherein bombs are dropped

Some of you will have spotted the problem already, but don't feel bad if you haven't. It's a complex tree that you can't really fit in your mind all at once. I'll give you a clue, read the leaf nodes left to right. Yup, that is our complete, grammatical sentence. Doesn't that strike you as a bit odd? Well, it shouldn't really, as here is the problem. Although the tree structure is supposed to be universal people want it to do too much. They want it to define how words fit together semantics and syntax. Because they're greedy.

The upshot of this little decision is that for even moderately complex sentences the tree has to be completely re-ordered to make the leaf nodes read out correctly. Two sentences with identical meaning could be encoded with very different trees. The concept of an inflectional phrase allows us to move the subject to the top left of the tree so it's always first. Now, even the linguists balked at this, so they decided there was a difference between where a node is and where it came from. This is called "base generation", a phrase can logically belong in part of a tree, but move to another to meet word order requirements.

In other words, there are a series of meta-rules for this universal grammar that tie it to a specific language. This theory suddenly becomes hopelessly inelegant, the tree might as well be replaced with a list of words for all the value it adds.

The lesson

Two simple, complementary theories are better than one complex one.  By putting too much stock in this tree representation it becomes ordered and language-specific.  Instead of a universal grammar we get an overly complex representation of a sentence in a single language and a false impression of universality.

Don't be a fool, demand relational grammar from your linguists.

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