How to assign multiple roles for capabilities array withini register_taxonomy function?

When assigning capabilities to ‘capabilities’ argument of register_taxonomy() you need to assign the capability and not the role! so use capabilities that only a specific role has eg:

'capabilities' => array (
            'manage_terms' => 'manage_options', //by default only admin
            'edit_terms' => 'manage_options',
            'delete_terms' => 'manage_options',
            'assign_terms' => 'edit_posts'  // means administrator', 'editor', 'author', 'contributor'
            )