The rules for written languages say that one needs a level of Artes Liberales for each writing system (defined by example as an alphabet), plus knowledge of a language normally written in that writing system.
That doesn't coincide very well with the way one learns writing. The initial idea of writing -- that written symbols can correspond with spoken language -- is a big leap of learning. But once one gets past that hurdle, a new alphabet is trivial.* The exception would be really complicated written languages -- ideographic writing systems such as Chinese and Egyptian hieroglyphic.
The requirement of the Educated virtue -- and perhaps a single level of Artes Liberales for the grammar -- seems sufficient to comprehend the basic idea "written symbols represent spoken language" well enough to read or write in a single written language. To learn an additional written language is fairly easy -- subject to the requirement that the learner must find a teacher who knows the new writing system. Learning from exposure doesn't do the job, because the average rabble can't read or write. Finding a literate language teacher is challenge enough.
Alternatively, one might learn a written language system from a written source meant for that purpose. For example, a magus is fluent in written and spoken Latin, and competent in spoken Arabic, but wants to learn written Arabic. To do so would require finding a tractatus on written Arabic, with explanatory text in Latin and a bunch of examples of written Arabic.
Very complicated written language systems, such as Chinese, are special cases. (Chinese isn't a great example because it's well beyond the bounds of Mythic Europe, but it's the most familiar in the modern world.) Alphabetic systems are -- at least to some degree -- approximate representation of the sounds of the spoken language. Written Chinese doesn't work that way -- it's a symbolic representation of the meaning of the words, with a great deal of idiom. To approximate it in game terms, I'd say it requires Educated (for the idea of writing), a single level of Artes Liberales (for the theoretical side of grammar), and then it works like an additional language, separate from spoke Chinese. Such a rule is probably moot unless a party travels far beyond the usual limits of Mythic Europe, however, unless such a language exists there that I don't know about.
Finally, I don't mean to take anything away from Artes Liberales. It's a useful skill even without its link to written languages. I just don't think that the game mechanic of one alphabet per level of Artes Liberales makes much sense.
- In the usual sense, not in the sense of the Artes Liberales trivium.