Hello kitten my old friend
I've come to give you food again
Because it seems while I was sleeping
Up onto my bed you came creeping
And the meowing that you planted in my ear
Woke me here
And caused the sound of munching.
Andrew Ducker found an article claiming that apes can't really use sign language, and that causes me to think about communication with animals, pet cats and dogs in particular.
True enough that, as the article says, my conversations with our cats are mostly about their wanting something. "Feed me! Pet me! Get me a peacock feather! Clean my litter box!" And that there is absolutely no syntactical grammar in any of this. So I wouldn't call it language. But it is communication.
For even if the cats can't give a complex account of their emotions, they clearly have emotions which express themselves in behavior and tones of meowing. And because we live a simple, well-organized life with regular expected events - and the cats get very disturbed when this is upset - they've learned to know whether the humans' actions are proceeding towards filling feline wants, even if there's no direct connection between those actions and those wants.
This second-order understanding is well-known among dogs. The dog gets excited at the prospect of a walk when it sees you going towards the closet, because it knows that that's where the leash is kept. That sort of thing. Cats, certainly those house cats that are responsive to human interaction, can grasp concepts at the same level of understanding.