Maybe closer to something for Worldbuilding SE?

@JosephWeissman I don't think they know about Berkeley's subjective idealism there.

I edited your post by adding (what I think is) implied context. If this does not agree with your intentions you can roll back the edit. Your proposed vocabulary suggests solipsism rather than subjective idealism, but the description of the first paragraph (Wikipedia's) would fit objective idealism just as well. Do you mean something like Berkeley's, Kant's or Fichte's idealism?

@Conifold Berkeley's

Berkeley was not a solipsist, this "I" has no special significance (it does for Fichte, where it "constructs" the world). "To be is to be perceived (or to perceive)" includes other souls and God. So you'll get a vocabulary with thinking subjects, their perceptions, and "passions and operations of the mind", not unlike Husserl's phenomenological vocabulary.

@Conifold Right. My mistake. So Berkeley's subjective idealism is not what I meant. I am probably closer to Fichte's.

@Conifold It sounds like you have enough raw matter to make an interesting answer.

@Bob I think that is of little or no significance to incorporate a pronoun like "I", as I think in my opinion, that the content of the "I" is reducible to the first variable Qualia (Q). Same for the verb "Know" as it can be reduced to "Evident", "True" and "Believe" in a doxastic and deontic sense.

@Bob , But on the other hand, the verb know is not to be merely a subjective notion in Epistemology , as the act of "knowing" has an element of truth and evidence to it. Two components that are objective (True, Evident) ...and one subjective component (Belief) ... And this is only the naive definition of knowledge (I did not consider Gettier's problem). Therefore, one should note that the verb "Know" is not completely subjective, and therefore cannot be used in a subjective idealist thesis.

@Bob , and if you redefine and analyse in logical symbols, the objective components "True" and "Evident" as merely being subjective phenomena that compose the verb "know", then I don't see how one might distinguish between "believing that you saw red in a dream" and "knowing that you saw red while awake". So, it follows that it would be useless for such an analysis to include "know" or similar verbs that have an element of truth and evidence to them.

@SmootQ Subjective idealism allows for knowing that I have such and such subjective experience (such as seeing-red, possibly in dream) at the moment I have it. But I cannot know anything about a supposedly-external world because for that I would need to know that I am not dreaming or hallucinating (cf. Descartes' first meditation).

@Bob in that case, you would have to redefine the Actual World, "True" and "Evident" . In traditional terms, the actual world includes both the subjective and the objective. In Modal Logics, one can infer "P is true in some possible world" from "It is possible that P" , regardless of whether P is (Red in a dream) or (The king is bald)...etc. In a subjective system, one would find a way to redefine propositions so that they only have a subjective meaning... And the logic will also change slightly

@Bob And don't forget that propositional logic sometimes fails with subjective phenomena

@Bob As for dreams and hallucinations, you somehow 'know' that they are not as true as your wakefulness , which means that you will also need to denote continuity and discontinuity as elements that can account for this 'subjective' sense of "know"

@Bob so, in symbolizing "True" and "Evident" in formal logical terms, you would have to rely on further notions like spatio-temporal "continuity" and "discontinuity" in time. As in dreams this continuity is broken, if you don't do that, well : your system would not distinguish between dreams and reality, and such a subjective system would fail

@Bob Another element I can think of, is the notion of "True", "False" and Possible. In a completely subjective realm, True would be taken to mean something that is both continuous in space and time (i.e not a dream), and that is actual (in the sense of being an element of consciousness). Therefore, a proposition like "The planet that is called Venus" SHOULD fail to denote in such a system, if "Venus" is not an element of a current subjective experience. So, A proposition P can be True in traditional logic, while it is False in a subjective idealistic system.

And temporal logic would also fail in the sense we understand it : in a subjective logical system, F and P (Future and Past) and H and G (has been always true, and will always be true) would always return false, since past and future are not part of the current subjective experience. Nevertheless, I think such a system would be interesting , although I am a materialist.

@SmootQ You seem to have more than enough matter to make an interesting answer.