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I have done this sort of experiment by listening to podcasts on the metro-- from that I know that "smida" is some sort of common, probably grammatical, particle in Korean.  From listening to Georgian, I can pick out the Russian loan words and proper nouns. From audio context, I learned from an Icelandic podcast how to say "call back, the phone connection is bad"

Xeno-interlangs are an application to this, if you are writing a known text to send to some who will need to decipher it, e.g Astrogloss, lincos, etc. http://en.wikipedia.org/wiki/Communication_with_extraterrestrial_intelligence#Mathematical_and_scientific_languages  They seem to think that in a message among people who don't have a common communication system, that they will at first want to discuss arithmetic. This discards the most valuable opportunity for context: the idea that if there is a message sender, there will be a sentient message receiver, who probably has to consume energy to survive, dies, reproduces, lives in a world of three dimensions with a past present and future, etc. Discussing arithmetic on a first encounter has to violate one of the Gricean maxims.

Also the instructions on the walls of nuclear waste facilities have a similar challenge, making sure that the "do not open" text is readable even after the collapse of civilization and a replacement of the surrounding communities' languages.

If I was going to do this and couldn't resort to pictures, I would use the context of the visible artifacts of writing as the common context.  For example, could you guess the meaning of this:

(blah) (blah) a
(blah) (blah) b
...
(blah) (blah) z
(blah) a (blah) z (blah).

was equal to ...

this is the letter a.
this is the letter b.
this is ...
this is the letter z.
Letters a through z are all the letters.

Similarly, adjacency, ordering, reverse ordering, containing, etc could be expressed through verbose and lengthy illustration. Taking these semantic primitives and building up to a useful message like, "We are from earth, do you have anything valuable to trade?" could be a real long task.

And so on.  Human brains are incredibly skilled at mapping messages to context, just think of the feat that Hellen Keller had to pull off, learning a language without the common context of pictures or sound.

Matthew Martin