According to my UML teacher formal means strictly according to rules, officially and how it's supposed to be. He says a formal language = syntax + symbols + spelling. Another term he uses is deterministic. According to him it means "strictly predictable", which means its only interpretable in a single way. So one input can't map to two outputs.
If I'm given any example of a language that humans invented, I can't tell nor elaborate whether it's a formal language or not. Some of these examples are natural languages (English, French, Dutch, etc.), UML, Math, notesheets, programming languages, markup languages, braille.
In my teachers powerpoint presentation, he explained a natural language is not formal because it's dependent on context (Unless I understand the definition of "deterministic" wrong, deterministic is the opposite of context dependency. By context dependency I mean, a sentence or a word can have two different meanings, e.g. You were right. But also Make a right turn at the light Thus a natural language is not deterministic).
But then a few slides later he said a formal language doesn't have to be deterministic, which makes me wonder why he would use context dependency as an argument to explain formal languages in the first place.
What makes a language formal? Perhaps you can elaborate by using the examples given above. And what makes a language deterministic? Is it correct that deterministic is the opposite of context dependency?
N.B. Wikipedia isn't making much sense to me, and I've read that the article about formal languages is quite a mess because people have different opinions on it.