In addition to a pretense box, Stich and I propose a mechanism that supplies the pretense box with representations that initiate or embellish an episode of pretense, the “Script Elaborator”. This is required to explain the bizarre and creative elements that are evident in much pretend play. However, there are also much more staid and predictable elaborations in pretend play. This too is well illustrated by Leslie’s experiment. Virtually all of the children in his experiment responded the same way when asked to point to the “empty cup”. How are these orderly patterns to be explained? In everyday life when we acquire new beliefs, we routinely draw inferences and update our beliefs. No one knows how this process works, but no one disputes that it does work. There must be some set of mechanisms subserving inference and updating, and we can simply use another functional grouping to collect these mechanisms under the heading “Inference Mechanisms”. Now, to explain the orderly responses of the children in Leslie’s experiment, we propose that the representations in the pretense box are processed by the same inference mechanisms that operate over real beliefs. Of course, to draw these inferences the child must be able to use real world knowledge about the effects of gravity and so forth, and so Stich and I also suppose that the inferences the child makes during pretense can somehow draw on the child’s beliefs.
This is, I think, a fairly typical statement of one important respect in which belief is often said to be similar to imagination: each is subject to the same inference mechanisms. Nichols includes this chart:

Notice the 'inference mechanisms' that act on beliefs and imaginings alike.
Now I can see well enough that pretense and belief inferences tend to go in the same way. If I know full well that p only if q, and believe p, I'll often come to infer to a belief that q, just as, if I imagine p, I'll often come to infer to imagine q. (Modulo various familiar complications: sometimes I give up the previous belief, etc.) But doesn't just the same thing happen with desire? If I desire that p, and know full well that p only if q, I'll very often, through a very ordinary sort of means-end reasoning, come to desire that q, modulo various familiar complications like the possibility that I'll stop desiring p.
Take a background situation where I know that nothing funny is going on with the cups; gravity is normal, the water is liquid, etc.
Suppose I believe the cup had water in it and has been turned over. Then I'll believe that the cup is now empty.
Suppose I imagine or pretend that the cup had water in it and has been turned over. Then I'll imagine or pretend that the cup is now empty.
Suppose I desire that the cup had water in it and has now been turned over. Then I'll desire that the cup is now empty.
This suggests to me that the similarities between imagination and belief, in contrast with desire, are exaggerated by, e.g., the diagram above. Those inference mechanisms apply to desires just as well as to beliefs and pretenses. Are there similarities in inference mechanisms that distinguish beliefs and pretenses/imaginings from propositional attitudes more generally?