Good questions. "De kat drinkt zijn melk" is indeed an ambigious sentence. It can mean that the cat drinks his own milk, and also that the cat drinks Bob's milk. (However, without a context, the real meaning is probably the first one...). The same ambiguity exists in the plural: "De katten drinken hun melk" can mean that the cats drink their own milk, or that the cats drink Bob and Alice's milk. Mind you,there is no ambiguity in the sentences "De kat drinkt hun melk" (The cat drinks their milk) and in "De katten drinken zijn melk" (The cats drink his milk).
In Belgium we would only use 'zijn melk' if we know for certain it is a male cat. Otherwise it would refer to someone else's milk. The word 'cat' is considered to be a feminine noun. But I guess this is less important for people learning Dutch. It is difficult enough to know when to use 'de' or 'het'. The fact that 'de kat' is a feminine noun and 'de hond' (the dog) is a masculine noun is less important. This distinction is slowly disappearing in the language anyway, especially in the Netherlands I guess.
Is it also ambiguous in Dutch as to whether the cat is drinking his own milk or is drinking Bob's milk?
Thanks for replying, but I still don't think I understand this - I'm not sure what you mean by it can only be used in specific situations. Their cannot be used if the subject was he, she or it, but it can be used for any other singular subject, such as the cat in this sentence. The English sentences the cat drinks its milk and the cat drinks their milk can have the exact same meaning.
Usually in English we use its for an animal and/or inanimate objects (when singular) as far as I know. Particularly in this sentence because the cat's gender isn't known to anyone, we aren't referring to it as a pet and nor do we know the cat's name :)
Also because the cat isn't plural, I find it feels unnatural to say "the cat drinks their milk", if it was several cats drinking milk you could say "the cats are drinking their milk". It may be used in spoken or colloquial English (it sounds odd to my ears, personally and I've never heard it) but I've looked it up on several different websites which all have its when referring to a singular animal (one website even has an exercise where it says the following - in a fill the gap exercise - : 4. That poor dog has lost one of its legs)
But as far as I'm aware:
We use its when the animal is singular and the name/gender of the animal isn't known. Nor is it known if it's a pet.
So: the cat drinks its milk
Or "What is the cat doing?
It's drinking its milk.
But if the cat's gender is known and it's a pet of ours we say:
The cat drinks his/her milk
But when plural:
We use their as it's considering the group of cats as individuals.
The cats [are drinking/drink] their milk
Think of it as the difference between a group of people like a football team and then a company. A company is a single entity so you use its whilst a football team is made up of a group of individuals so you'd use their
I hope that sheds some light on it, as I've never really heard the usage of their in that way when it's on about one animal drinking milk that belongs to them, although I think the exception is if you use it in a context where the cat is drinking someone else's milk (perhaps the neighbours),
e.g What is that cat doing over at the Smiths house?
It looks like it's drinking their milk
In which case the their here refers to the fact that the milk belongs to the Smiths and not the cat. With a little bit of context, then you possibly could use their but I don't think it's natural to usee with a singular animal.
Your usage may even be regional, I'm not sure but from what I've looked up, I've not heard of it used in that way :) I hope my explanation is okay, and if there are solid and grammatical explanations online which give examples to your usage please feel free to link them (I'm not saying your usage is completely wrong by the way) ^_^
Have a wonderful day :)