One difficulty in al-Sakkākī’s wording is whether assignment means only established literal designation or sometimes an interpreted extension created by rhetorical claim. If both are left open, additional restrictions appear necessary.
One response is to understand an unqualified reference to assignment as the actual convention determined by the relevant discourse. Restrictions such as “interpretation” and “actually” can then address a particular metaphor theory that imagines the target within the source’s class.
Still, a well-formed definition should use its central terms consistently. Otherwise the objection and response may merely alternate between different meanings of the word “assignment.”