I’m surprised that nobody has mentioned the logic of belief revision. It would seem to me that to forget a statement (that you previously believed) is to have your belief set contracted by it. When you lose a belief by learning something else (e.g. reading the newspaper) you are revising your belief set with new information.

Cases of forgetting are usually dissimilar to cases of learning the negation because to forget something is not to proclaim false what one once believed true, but to proclaim indetermined what one once believed true. When it is Tuesday, people who forget what day it is have not “learned” that it is not Tuesday but come to have less credence that it is Tuesday.

I also think that as forgetting is an irrational process that afterwards our belief set may not be coherently closed under logical consequence. For example at t1 I may believe the following:

If A then (B and C)
A
B and C

I then forget B, i.e. I come to have no opinion about B. Now I should ordinarily come to believe that (given C) if B then A. As A depends on the truth of B and C, and I have come to doubt B, I should assert that If B then A. But probably because I irrationally forgot B I may come to still believe fully in A. Not realising that I have forgotten B means that I don’t realise I have lost a supporting foundation for A, so I continue to believe it.

I don’t think the failure to close your belief set deductively is necessary for forgetting, but it is a common addition. I suppose that if a computer or perfectly rational being forgot something it would affect the rest of its belief set.

Ben reads an email saying the bridge he normally crosses while driving to work will be closed and he infers that he will have to take a different route tomorrow. Tomorrow arrives and he heads toward the closed bridge, failing to remember that it was closed. He arrives at the closed bridge, slaps himself on the forehead and says “I knew the bridge was closed”. Or alternatively he says “I forgot the bridge was closed”. Both seem true. One issue is the temporal reference of the “knew” in this attribution. Did he only mean that he knew it when he read the email, or does he mean that he really knew it all along? I’m inclined to think the latter.

But it’s still not clear to me that most cases of forgetting will be in line with the “loss of memory trace” examples; there can be cases where I forget something for a whole day, and even affirm the opposite, before I remember and say, “Oh yes, I did lock the door behind me; I remember doing it now.” We wouldn’t say that, when I was protesting that I didn’t lock the door, I believed that I had. But the memory trace was still there; perhaps buried a bit deeper than in the “forgot for a moment” cases, but it doesn’t seem to me that it’s a difference of degree.

I also think, pace Gabriele, that we’re going to need to look more closely at the concept of belief if we’re going to try to regiment cases according to whether you still believe something but can’t consciously recall it; these cases seem to me like cases in which you believe it in one sense but not another.

I’m sort of in this Williamson camp that belief constitutively aims at knowledge; it’s therefore ultimately normative. In terms Williamson wouldn’t agree with: it’s analytic that non-knowledge belief is defective.

For not-unrelated reasons, I don’t see that it’s helpful to try to regiment out, for example, belief, in non-epistemic terms. (But I don’t object to oversimplifications for introductory students; I see the value in teaching the way you suggest.)

I know there’s this tradition that the non-belief states that are relevant to epistemology (e.g. perceptual seemings) aren’t rationally evaluable; but I’ve never found it compelling. There are good and bad ways for lower-level visual processing systems to generate seemings, just as there are for higher-level cognitive ones to generate beliefs. I don’t see why the epistemologist can’t consider all of these valuations.

If I had a state of mind and then experienced this state of mind at another time with an accompanying new component of the state that indicates “I remember this” then I have remembered the previous state. If I do not have a state of remembering a previous state when challenged at a particular time then I have forgotten it at that time.

This would seem to minimise the number of undefined components in the problem so that only “mind” is mysterious. In the other analyses above we have “belief”, “knowledge”, “cause”, “memory trace” as mysterious, difficult to define entities.

I would guess that this proliferation of entities is due to an acceptance of irrational arguments against the existence of mind. See Blind Willie Johnson’s thoughts on this matter.

Of course, I don’t mean to deny that the notion of belief is a central notion in epistemology and I have no problems with calling it an epistemological notion but I don’t think that this alone makes it distinctively epistemological (btw, I’m not sure in what sense you think ‘belief’ is a normative notion, could you expand a bit on that?).
This is the (admittedly simplistic) story that I usually tell my students on the first day of an epistemology class when explaining the JTB analysis of knowledge. If they want to find out more about epistemic justification (and knowledge) then they are taking the right class, but, if they want to find out more about what is for S to believe that p or for p to be true, then they’d better take, respectively, a philosophy of mind course and a metaphysics course (or maybe philosophy of logic course?). So, the simplest (and most simplistic) way to put the point I was trying to make is probably that, insofar as epistemology is concerned with changes in someone’s doxastic state, it is concerned with those changes to doxastic states that that are subject to evaluation in epistemically normative terms (or if you want with the reasons not the causes of the change) and, as far as I can see, forgetting doesn’t seem to be one of those changes because it is a change that occurs for a cause that is not a reason. (My intuition is that, whereas we might take one to be legally or morally responsible for forgetting that p in some cases, we wouldn’t take them to be epistemically responsible.)