following some search that I've just done it looks that rs232 is the protocol and ttl a standard and in fact we will be using both here: http://answers.yahoo.com/question/index?qid=20090211134205AApzAvY
following this we will be using the rs232 protocol with the ttl voltage levels.
and it looks very common to be like this...
EDIT: Aborting this idea since the baud rate of the nspire is 115200 it's too high to a picaxe microcontroller. I don't know if the nspire's baud rate can be lowered or it the arduino supports such a high baud rate.
Anyone here knows?