Edit line 39 of /wp-content/plugins/advanced-access-manager/extension/AAM_Activity_Log/extension.php.
Replace
require_once(__DIR__ . ‘/activity.php’);
With
require_once dirname(__FILE__) . ‘/activity.php’;
Reason for the error:
__DIR__ is new in PHP 5.3. For php version 5.2.17 and older, __DIR__ will not work. For older version of php, dirname(__FILE__) works perfectly.