Put your category id’s in an array format. Like the below one.
$cat_related = query_posts( array(
'post_type' => APP_POST_TYPE,
'post_status' => 'publish',
APP_TAX_CAT => $string_array,
'ignore_sticky_posts' => 1,
'paged' => $paged,
'post__not_in' => array($post->ID),
'category__not_in' => array ( $store_id )// this is STORE ID
) );