Truth is not belief - already covered:
Truth is a unary. T(p) is a general representation of the statements, propositions, sentences, facts, or whatever you will, that we cast as true: "p is true"
Belief is binary. B(x,p) is a general representation of the statements, propositions, sentences, facts, or whatever you will, p, that we cast as being believed by x. "x holds that p is true"
— Banno
Further, one chooses between a realist and an antirealist grammar. The best grammar for cats and mats is realist. — Banno
This is about our accounting practices. It restricts and/or limits all belief to propositional attitudes. While this is little to no problem at all if we're talking about language users who have and or develop propositional attitudes, it is quite problematic if we're talking about creatures that are incapable of having a propositional attitude but are perfectly capable of believing that a mouse is behind the tree, that a lizard is under the stove, that a dog is in the house, that food is in their food bowl, or that another cat is on the bed. So, while it works well for analyzing belief statements, the grammar of belief being put to use here is inherently inadequate for taking proper account of language less creatures' belief. It's found lacking in explanatory power.
Cats do not have an attitude towards propositions. They do not hold propositions as true. The T sentence cannot properly account for creatures incapable of having propositional attitudes, and thus, we cannot rightfully encapsulate a cat's belief within quotes on the left side as we do with language users for that would be a mischaracterization of the cat's belief(an accounting malpractice when used in such a way). However, and this is very interesting to me, when we do talk about what it would take in order for a cat's belief to be true, we find ourselves saying much the same thing as we do when it comes to propositional attitudes, despite the fact that cats are incapable of having and/or developing them.
Cookie's belief that a dog is in the house is true only if, only when, and only because a dog is in the house.
Such are the kinds of belief that some language less creatures are capable of forming, having, and/or holding. Much like us, they are more than capable of forming, having, and/or holding belief about what's going on around them. Unlike us, they are incapable of talking about their own thought and belief as a subject matter in its own right. Unlike us, they are incapable of considering what sorts of things can be true, and what it takes in order for them to be so. Unlike us, they are incapable of doubt and/or skepticism. Much like us, they are capable of forming, having, and/or holding true belief, false belief, as well as belief that is neither at the time(in the case of expectation).
Again, I find it very interesting that our analysis of what sorts of things can be true and what makes them so has no issue at all exhausting some language less creatures' belief, so long as it's not formal logic being used. Common language works just fine.