Principle A is a statement in the government and binding theory of syntax that is intended to answer questions such as these: Why in sentences such as the following must 'Mary' and 'herself' refer to the same individual in the first case? Why isn't the second sentence grammatical? Why can't 'Mary' and 'herself' refer to the same individual in the second case?
Maryi saw herselfi in the mirror
*Herselfi saw Maryi in the mirror

Possible (wrong) easy explanations

Linear order: 'Mary' and 'herself' have to occur in left-to-right order. When they do, 'herself' takes 'Mary' as its antecedent.

The following show that this cannot be right. Even though 'Mary' and 'herself' are in the supposedly correct order, and 'father' is not a possible antecedent for 'herself', still the sentence is bad. Note also that on the most likely interpretation it seems to imply that Mary's father is female. This suggests that despite the implausibility of this interpretation, somehow 'herself' is taking 'Mary's father' as its antecedent. In the second sentence the two key terms appear in the supposedly correct order, but still something is amiss. What?


*
Maryi's father likes herselfi
*The book about Maryi fell on herselfi

Subjecthood: Perhaps, we might think, it is critical that 'Mary' be the subject of the sentence. But even when 'Mary' is not the subject, there are grammatical sentences where 'Mary' and 'herself' successfully corefer.

John likes Maryi's picture of herselfi

What sort of relationship?

How can we correctly describe the necessary relationship between anaphors (like 'herself') and their antecedents? To state the relationship we need to define several terms, the most critical of which is c-command.

Definitions:

c-command: Node X c-commands Node Y iff (if and only if) the first node dominating X also dominates Y.
co-indexing: Nodes are co-indexed if each carries the same subscript.
bound: An NP is bound iff it is co-indexed with a c-commanding NP.
free: Not bound.

Principle A applies to:

Maryi saw herselfi in the mirror

      S
     / \
  NP     VP
  |    /    \
  N   V      NP
Mary saw    /  \
           N    PP
       herself  / \
               P   NP
              in  the mirror
John likes Maryi's picture of herselfi
        S            
      /   \          
    NP     VP
   /      /  \
  N      V    NP
John  likes  / | \____
           NP  N      PP
           | picture /  \
           N        P   NP
         Mary's    of   | 
                        N
                      herself

*Maryi's father likes herselfi

These are difficult to draw, so I switch to a different but logically equivalent form now...

(S
 (NP
  (NP
   (N Mary's))
  (N father))
 (VP
  (V likes)
  (NP
   (N herself))))
*Herselfi saw Maryi in the mirror
(S
 (NP
  (N herself))
 (VP
  (V saw)
  (NP
   (N Mary))
  (PP
   (P in)
   (NP
    (Art the)
    (N mirror)))))
*The book about Maryi fell on herselfi
(S
 (NP
  (Art the)
  (N book)
  (PP
   (P about)
   (NP
    (N Mary))))
 (VP
  (V fell)
  (PP
   (P on)
   (NP
    (N herself)))))

"An anaphor must be bound"

If this is correct, then it should predict which of the above sentences is grammatical and ungrammatical -- under the specified interpretations. We have a problem, however:

*Maryi thinks the boy saw herselfi

(S
 (NP
  (N Mary))
 (VP
  (V thinks)
  (S
   (NP
    (Art the)
    (N boy))
   (VP
    (V saw)
    (NP
     (N herself))))))
This indicates that we must modify the principle as follows:

An anaphor must be bound in its own clause.

Note: Anaphors MUST have an antecedent in the sentence. If "herself" in the following sentence is taken to mean someone not mentioned in the sentence, the sentence is ungrammatical.

*Maryi saw herselfj in the mirror

(S 
 (NP
  (N Maryi))
 (VP
  (V saw)
  (NP
   (N herselfj)
   (PP
    (P in)
    (NP
     (Art the)
     (N mirror))))))

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