I should also note that this behavior isn't even consistent:

+---+----------------+------------+----------------+-------------------+----------+
| # | file           | includes   | should include | actually includes | correct? |
+---+----------------+------------+----------------+-------------------+----------+
| 1 | /root/a.php    | b/b.php    | /root/b/b.php  | /root/b/b.php     | yes      |
| 2 | /root/b/b.php  | b2.php     | /root/b/b2.php | /root/b/b2.php    | yes      |
| 3 | /root/b/b2.php | ../c/c.php | /root/c/c.php  | /c/c.php          | no       |
+---+----------------+------------+----------------+-------------------+----------+

Behavior 1 works as it should
Behavior 2 works as it should
Behavior 3 works not as expected

Behavior 2 and 3 are inconsistent with each other.

It's working just like it is supposed to be working.
The working directory (cwd) is the one for the 'main' script, a.php in your case. NOT the directory where the 'sub' scripts are located.
 

I posted this comment before but it seems to have evaporated. Is there a bug in the bug database? 



The problem lies with function php_fopen_with_path in
php-src/main/fopen_wrappers.c

The code is inconsistent with the what the documentation suggests (which
is c-like behaviour). And since I think the documented behaviour is more
intiuative, the code appears in-correct.

Currently, the code is as follows:
If the filename starts with a '.' (such as "../c/c.php" above), the
function looks for the file relative to the 'main' script.
Else if the filename is an absolute path, the function opens it
directly.
Otherwise, the function looks for the file relative to the directories
listed in the 'include_path' configuration directive.
If that fails, it then checks relative to the directory of the currently
executing script.

This has the consequences stated in the initial bug report. It also
means that relative includes are always enabled. Adding a '.' path to
the paths in include_path does not enable relative includes. It causes
PHP to check relative to the 'main' script before checking relative to
the currently executing script.

I think it would be better if the function:
Opens the file directly if it is an absolute path.
Otherwise, scan the 'include_path' directive and replace a '.' path with
the path of the currently executing script.
Look for the file relative to the directories listed in the modified
'include_path'.

I've got the same problem (The relative inclusions always take the requested page for directory reference.) on WinNT/php4.3.2 newly installed, but strangely I hadn't with WinNT/php4.3.0

A workaround found at http://fr.php.net/manual/fr/function.include.php is to use

require(dirname(__FILE__) . "\..\second.php");

Same problem here.. 
 
PHP 4.3.7 under Redhat 7.3 (compiled into apache).

Thank you for your bug report. This issue has already been fixed
in the latest released version of PHP, which you can download at 
http://www.php.net/downloads.php

I think this is already documented:

http://www.php.net/include: "Files for including are first looked in include_path relative to the current working directory and then in include_path relative to the directory of current script. E.g. if your include_path is ., current working directory is /www/, you included include/a.php and there is include "b.php" in that file, b.php is first looked in /www/ and then in /www/include/."