This isn’t really new information, but I thought just for clarification I’d sort of say again some things about what modal bases are.

A sentence like Pat might have eaten the sandwich can be true or it can be false, first of all.

The modal base is basically a set of worlds the comparison is being made with — so Pat might have eaten the sandwich would be false if it turns out that in none of the worlds in the comparison set are ones in which Pat has eaten the sandwich is true. A modal takes the comparison set and asserts something about how many of those worlds have the property that the rest of the sentence is true. So, Pat must have eaten the sandwich asserts that Pat has eaten the sandwich is true in all of the comparison worlds, Pat might have eaten the sandwich asserts that Pat has eaten the sandwich is true in at least one of the comparison worlds, Pat probably ate the sandwich asserts that Pat ate the sandwich is true in more of the worlds in the comparison set than it is false in, and so forth.

The comparison set itself can differ as well—that’s where the concept of modal base comes in. If you’re just comparing basically all of them, that’s the root modal base, and it would have the meaning of “capable” essentially (Pat can lift a piano). You can also limit it to just those worlds that you believe are candidates for the actual world—that is, those worlds that are consistent with your beliefs. That’s the epistemic modal base, and has a meaning something like “as far as I can tell” (Pat must have lost his keys). Then, there’s one that limits the comparison to just those worlds in which some kind of rules are being obeyed—this one is the deontic modal base, and it will generally carry a “permission” or a “judgment of propriety” kind of meaning (Pat may leave class early, Homework must be turned in on time).

So, Pat might have eaten the sandwich can be true, even if Pat has eaten the sandwich is false in the actual world. What it requires to be true is (assuming the epistemic modal base) that at least one of the worlds that you believe are still candidates for being the actual world, based on what you know, is a world in which Pat has eaten the sandwich. That it is not inconsistent with your beliefs that Pat ate the sandwich.

There are a number of things I believe, and so that divides all of the possible worlds into those that are consistent with my beliefs and those that are not. The epistemic modal base is the set of worlds that are consistent with my beliefs. However, there is also the possibility that I believe something that isn’t in fact true. So: if I believe p and q, but p is actually true and q is actually false, then the epistemic modal base would be all of those worlds in which p and q are true, but the actual world won’t be among them.

So, from the handout, what I believe is true is basically defining the epistemic modal base—all of those worlds in which my beliefs are true. Within those worlds, some are worlds in which Pat has eaten the sandwich and some are worlds in which Pat has not, assuming that I don’t have a belief about Pat eating the sandwich. (If you believe Pat ate the sandwich, then it would be only those worlds in which Pat ate the sandwich that are in the epistemic modal base, and the sentence should be Pat must have eaten the sandwich instead).

I don’t know if that makes it any clearer, but perhaps.