Lera Boroditsky is one of the premier researchers on this topic. They've also done some excellent work on comparing spatial/time metaphors in English and Mandarin (?), showing that the dominant idioms in each language affect how people cognitively process motion.

But the question is more broad -- whether some form of natural language is required (natural, roughly meaning used by a group in day to day life, is key here)? Differences between major natural languages are for the most part relatively superficial and translatable because their speakers are generally dealing with a similar reality.