User role permissions based on taxonomies

You might be able to use the filter user_has_cap which is used when checking for a particular capability (found in /wp-includes/class-wp-user.php in has_cap):

    /**
     * Dynamically filter a user's capabilities.
     *
     * @since 2.0.0
     * @since 3.7.0 Added the user object.
     *
     * @param array   $allcaps An array of all the user's capabilities.
     * @param array   $caps    Actual capabilities for meta capability.
     * @param array   $args    Optional parameters passed to has_cap(), typically object ID.
     * @param WP_User $user    The user object.
     */
    $capabilities = apply_filters( 'user_has_cap', $this->allcaps, $caps, $args, $this );

So it would be something like:

add_filter('user_has_cap','check_post_taxonomy',10,4);
function check_post_taxonomy($allcaps,$caps,$args,$user) {
    global $post; if (!isset($post)) {return $allcaps;}

    $group = get_user_meta($user->ID,'special_edit_group',true);
    $taxonomy = 'taxonomy_'.$group; // maybe set to a, b or c?
    $terms = get_the_terms($post->ID,$taxonomy);

    // if there are no terms, remove the user capability(s) for this check
    // you may have to experiment to remove all the ones you want to
    if (!$terms) {
        unset($allcaps['edit_properties']);
    }

    return $allcaps;
}

I have done it this way because I realized the logic of the question is not quite right. If a post type has taxonomy A, B and C assigned to it, even if you set these capability filters for the role groups as you say, all three role groups would be able to edit anything in this post type anyway. In other words, there is no case where taxonomy A, B or C is “not” actually assigned.

Instead, I think you are really meaning “check whether this particular post has any terms assigned to it in taxonomy A”… and if so along group A to edit it, and so on. (Note: I have no idea if the above code will actually work for this case, it might need some more work. For example, currently this is checking for a user meta key for the group rather than an actual role/group.)

Related Posts: