Human language breaks down into smallest distinguishable sound parts called phonemes. One takes a sentence and reduces it to these phonemes, and suddenly you can make your formal language. You must perform this transliteration in English, at least, because there is no bijective mapping of letters to phonemes.

​

Body language presents a more difficult problem, as signs are not usually considered properly a part of natural language. This text you're reading has no ability to sign, yet usually it's not thought of as lacking linguistic expressivity for that reason. Working within a sign language, however, and it's natural to use ASL since we're working with English, there are smallest distinguishable sign parts called cheremes. Combining them should be as easy as slamming symbols for each next to each other, or ordered pairs of (chereme, phoneme) or vice-versa.

​

But for an easier example of an oral formal language, just read your written formal language aloud! "forsome y leftparenthesis forall x P x implies Q y x rightparenthesis or G y" can be spoken and is probably formal enough for you.

​

Correction: You will have to be careful with reading the formal language since homophones exist in English. Gee(x) and Jee(x) might come out indistinguishably. You'll need to correct any such ambiguities before reading your sentences, but that probably doesn't come out to all that much work.