I often see 'conversely' being used when the meaning is to express the 'contra-positive'.
I know that the contra-positive of a statement is logically equivalent to the statement, but they're still different formulations in natural language.
Question(s): In general, is there a more natural sounding word to use instead of 'contra-positively' in (informal but possibly academic) written English? If not technically, then what could be a good alternative?
(Just as a made up example: If I am standing up, then I am awake. Contra-positively, If I am not awake, then I am not standing up.
'Conversely' would sound natural but feels wrong since it has such an otherwise specific meaning (in logic). Perhaps it is used more loosely in natural English, and I am being overly cautious.
None of the often proposed synonyms of different thesaurus searches feels natural to put instead, e.g. 'contrary' or 'oppositely'.)
Edits: The comments about my initial example being bad are all fair, which is why I (after several edits) instead chose to reformulate the question completely. (It was really more what got me thinking than a good example anyway.) I hope it is a bit more clear now. Also, I think the answers already provided are sufficient.