Add Parent post category with hook/filter

Hi there,
I am using the "post category" field to populate the category of a post. This works well. What I would like to do though is:
if a child is chosen on the form, then the parent (or even parents) are added automatically with the help of a hook/filter. Which would be the best filter to use and how would I go about adding that parent to the post category?
In logic I would:
1. get the field value of the post category field into $child_category
2. use get_category_parent ($child_category) to save parent in $parent
3. wp_set_post_terms ($post_ID, $parent, $category, true)

Do not know if that is right though. If it is the questions I have: what do I use for $post_ID and what do I use for $category?
As always, any help is appreciated!

Hi Dave,
I used the following code and it works great! Thanks for your help/pointers!!!

// select parent term automatically for the 'project_type' taxonomy in form #1
add_action('gform_after_submission_1', 'gform_parent_category');
function gform_parent_category($entry) {

	$created_post = $entry['post_id'];
	$child_ID = $entry["7"];
	$term_object = get_term_by('id', $child_ID, 'project_type'); // replace project_type by chosen taxonomy
	$parent_ID = $term_object -> parent;
	wp_set_post_terms( $created_post, $parent_ID, 'project_type', true ); //replace project_type by chosen taxonomy
}

But instead of copying the code for each form, I wanted a flexible solution: I tried to use wp_get_post_terms instead. The only problem is that function returns an empty string! No idea why?!? Quite messy code as I tried different options:

add_action('gform_after_submission', 'gform_parent_category');
function gform_parent_category($entry) {

	$created_post = $entry['post_id'];
	$post = get_post($entry["post_id"]);
	//$child_ID = $entry["7"];
	//$term_object = get_term_by('id', $child_ID, 'project_type'); // replace project_type by chosen taxonomy
	$query_taxonomy = 'project_type';
	$term_object = wp_get_post_terms($created_post, $query_taxonomy, array("fields" => "all")); // replace project_type by chosen taxonomy
	$product_terms = wp_get_object_terms($created_post, 'project_type', array("fields" => "all"));
	$parent_ID = $term_object -> parent;
	print_r($term_object);
	var_dump($term_object);
	var_dump($product_terms);
	var_dump($post);
	//$parent_ID = $term_object[parent];
	echo $parent_ID;
	wp_set_post_terms( $created_post, $parent_ID, 'project_type', true ); //replace project_type by chosen taxonomy
}

Have you got any clues?

This behavior can be achieved globally with a wordpress hook. There is no need for the 'gform_after_submission' hook.

Copy this: http://pastebin.com/tcvfg9L9

If you're using default posts try hooking to the action 'save_post', 'publish_post' or 'edit_post', etc. If you're using a custom post type, instead do 'save_my-post-type', where my-post-type is your post type's slug.