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I'm talking about the panels with lots of colored symbols on them you sometimes see in documentaries and the like. Apes point at the symbols in a specific order and in this way can communicate with humans.

I already googled around a lot, but wasn't able to find any detailed explanation on how exactly the language works (meaning of all the symbols, grammatical structure of the language and so on). It might just be because I don't know what words to use for my search, so can anyone with more expertise in the field point me in the right direction?

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The best article I found was this one. In it it says among other things that:

Kanzi, an unusually intelligent Bonobo chimp trained at Georgia State University, was remarkable in that he learned to use around 200 symbols on a portable electronic symbol board, a computer with buttons in the shape of absolute arbitrary symbols rather than manual signs. More interestingly, Kanzi learned how to use this board while watching his foster mother, Matata, being taught by traditional reinforcement methods. So Kanzi did learn how to use arbitrary symbols without being taught, although he did observe direct reinforcement of each symbol during the process and the symbols were taught one at the time.

The evidence for the mastery of syntax is not so convincing. While chimpanzees can learn to order their symbols to get what they want, it is not clear that they have mastered syntax. The reason is that when they initiate communication, even adult chimps often abandon the order they have learned and phrases such as, "Fight mad Austin," a famous utterance of Kanzi's friend Panbinisha. Here the order doesn't seem to matter. Apparently Panbinisha was trying to express, "there was a fight at Austin's and someone (Austin?) was mad". It is interesting that even human children simply don't make such errors once language acquisition begins, and certainly adult speakers would never utter such strings. Notice it lacks any morphemes (-ing, at, I, she, -ed), the hallmarks of grammar.

The trainer of Kanzi has published some materials but I do not know if they are available free online. You could probably send her an email and ask. The article goes on to state:

The maximum number of lexeme symbols (simple nouns, verbs, and adjectives) is interesting, too. The brightest chimpanzees master fewer than 200 of these symbols by adulthood. Human children know about 50 by the time they are 18 months old, when they begin learning nouns, verbs, and adjectives at the rate of about 5 per day. So the maximum achievement in symbol acquisition among other primates is more than matched by human children before the onset of language acquisition. In fact, the type of phrases spoken by chimpanzees and gorillas also resemble those spoken by children before they acquire their first language: "give orange" or "give Bobby orange" (without the pronoun me) are common expressions of children before the onset of language learning around the age of two.

The results suggest that while chimpanzees and gorillas are far more intelligent than anyone had imagined during the first half of this century, they are not capable of human language. Rather, they have a primitive version of the semantic ability children use before that explosion of language-learning around the age of two.

At least according to that article there is not much of a grammatical structure at all. The apes does not so much care about the order of the words either, even if the can learn a certain order, especially if they get something to eat if they do it right.

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