A generalization of Transformational Grammar and X' Theory formulated by Luigi Burzio that states:

If a verb has no specifier option, it cannot assign case.

Typical verbs have the following syntactic structure (sorry for the bad ASCII tree diagrams):

    VP
    /\
   x V'
     /\
    V  y
    |
   verb

Where 'x' is the specifier, and 'y' is the complement. There are special verbs however, such as subject raising verbs and past participles that do not contain the specifier, so they look like:
    VP
     |
     V'
     /\
  verb y

Examples of subject raising verbs are: fail, tend, and appear. Apparently one finds that wherever xbar theory predicts that a verb shouldn't have a specifier, that verb does not assign case. This phenomenon is found in other languages as well. This is important, because otherwise, we wouldn't be able to form some sentences.

Example:
Note, the example is a bit technical, and will probably be hard to understand fully without a working knowledge of Xbar Theory.

Burzio's Generalization is important for the formation of sentences such as "There fails to be a problem" because if fails could assign case, the sentence would end up being something on the order of "It fails there to be a problem."

In order to see why this is the case, it is important to trace how the sentence is built up. The following is the initial structure for the sentence:

    IP
    /\
   DP I'
      /\
     I  VP
     |   |
 {pres}  V'
         /\
        V  IP
        |   /\
    fails  DP I'
              /\
             I  VP
             |  /\
            to DP \
                |  V'
            there  /\
                  V DP
                  |  |
                 be  "a problem"

(notice that fails has a different structure from be, also, {pres} is a silent tense marker)
  1. Initially, the determiner phrase there would start at the end, so it would be roughly "to there be a problem". There is nothing there to assign case, and since every determiner phrase needs case, there moves to the next DP so the sentence is now roughly "there to be a problem".
  2. Now comes the crucial part. Ordinary verbs can assign the oblique case, so if fails were a regular verb, it would assign the oblique case to there. Now that if that were the case, there could finally rest because it would have been assigned the oblique case and a token it would be added on to the beginning of the sentence (first DP) so it would read "it fails there to be a problem." However, since fails is a subject raising verb (no specifier, governed by Burzio's Generalization), it cannot assign case to there so it ends up moving to the next available spot which happens to be at the beginning of the sentence.
  3. At this point, for reasons beyond the scope of this example, there receives the nominative case, and can stop there. We now have the correct sentence, "there fails to be a problem."

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