[personal response:]

> 1. I am a bit confused with the definition of TokenInfo and StringInclude.
> ...
>  <xs:complexType name="stringMatch">
>    <xs:sequence>
>      <xs:element ref="fts:tokenInfo"/>
>    </xs:sequence>
>    ...
>  </xs:complexType>
> ...
> follows that StringMatch can contain a SEQUENCE of tokenInfo. So, we
> have one-to many relationship.

I think you are misreading the Schema definition. The construct
    <xs:sequence>
      <xs:element ref="fts:tokenInfo"/>
    </xs:sequence>
doesn't mean "a sequence of any number of tokenInfo elements", it means "a sequence of exactly one tokenInfo element". To specify other than "exactly one", we would use the 'minOccurs' and/or 'maxOccurs' attributes (of <sequence> or <element>).

(By the way, if you have two independent comments, it's better to submit them as separate Bugzilla issues.)

[personal response:]

Re your point #2: Yes, I think that's a mistake in the specification.
Where we say:
    It is 1 for the first pair and 3 for the second in the first case,
    and 2 and 1 in the second.
We should instead say something like:
    For the first Match, the word distance between 
    the two TokenInfos is 3 (startPos 5 - endPos 2),
    and for the fifth Match, it's 2 (startPos 27 - endPos 25).

(In reply to comment #2)
But according to the spec: "the distance between the two is M2's starting position minus M1's ending position, minus 1.". 
So, for the first match we should get the distance = 5 - 2 - 1 = 2. Is it right ? 

By the way, section 3.6.3 contains example: 

"/books/book ftcontains "web" ftand "site" ftand
"usability" distance at most 2 words"

with the following explanation:

"The following expression returns false:

The search context does contain the phrase "The usability of a Web site", in which the tokens "usability" and "Web" have a distance of 2 words, and the tokens "Web" and "site" have a distance of 0 words, both of which satisfy the constraint distance at most 2 words. However, the problem is that "usability" and "site" have a distance of 3 words, which does not satisfy the constraint, and so the distance selection yields no matches, and the expression as a whole yields false. (The phrase "Improving Web Site Usability" would satisfy the given full-text selection, but it occurs in an attribute value, and so is not subject to tokenization.)"

But the spec says that we have to check the distance between "successive pair of matches"

So, we have to check the distance constraint for pairs: ("usability", "web") and ("Web", "site"), but not for the pair ("usability", "site")

This is followed from the formal function as well:

declare function fts:ApplyFTWordDistanceAtMost (
      $allMatches as element(fts:allMatches),
      $n as xs:integer ) 
   as element(fts:allMatches) 
{
   <fts:allMatches stokenNum="{$allMatches/@stokenNum}">
   {
      for $match in $allMatches/fts:match
      let $sorted := for $si in $match/fts:stringInclude          
                     order by $si/fts:tokenInfo/@startPos ascending,
                              $si/fts:tokenInfo/@endPos ascending
                     return $si
      where
         if (fn:count($sorted) le 1) then fn:true() else
            every $index in (1 to fn:count($sorted) - 1)
            satisfies fts:wordDistance(
                          $sorted[$index]/fts:tokenInfo,
                          $sorted[$index+1]/fts:tokenInfo
                      ) <= $n 
      return 
        <fts:match>
        {
           fts:joinIncludes($match/fts:stringInclude),
           for $stringExcl in $match/fts:stringExclude
           where some $stringIncl in $match/fts:stringInclude
                 satisfies fts:wordDistance(
                               $stringIncl/fts:tokenInfo,
                               $stringExcl/fts:tokenInfo
                           ) <= $n
           return $stringExcl
        }
        </fts:match>
   }
   </fts:allMatches>
};

So, is the example correct ? 

> [personal response:]
> 
> Re your point #2: Yes, I think that's a mistake in the specification.
> Where we say:
>     It is 1 for the first pair and 3 for the second in the first case,
>     and 2 and 1 in the second.
> We should instead say something like:
>     For the first Match, the word distance between 
>     the two TokenInfos is 3 (startPos 5 - endPos 2),
>     and for the fifth Match, it's 2 (startPos 27 - endPos 25).
> 

(In reply to comment #3)
> (In reply to comment #2)
> But according to the spec: "the distance between the two is M2's starting
> position minus M1's ending position, minus 1.". 
> So, for the first match we should get the distance = 5 - 2 - 1 = 2. Is it right
> ? 

Whoops, right, I forgot the minus one. So:
    For the first Match, the word distance between 
    the two TokenInfos is 2 (startPos 5 - endPos 2 - 1),
    and for the fifth Match, it's 1 (startPos 27 - endPos 25 - 1).

With respect to the prose around that example in section 3.6.3,
this problem was raised in Bug 5886 and has been fixed.
The revised wording will appear the next time the specification is published.

At its meeting on 2008-12-22, the Task Force accepted my responses in
comments #1, #4, and #5.

For comment #1, there is no change to the document.

For comment #4, I have modified the editors' copy of the Full Text
document as proposed.

For comment #5, there has already been a change to the document.

Consequently, I'm marking this issue RESOLVED-fixed.
If you accept this resolution, please mark the issue CLOSED.