Rather than continuing to try to ferret out what gleki has in mind, I will try to lay out what I take to be Lojban's (and occasionally logic's) position on part of the range of intensional propositional operators (modals, etc.)
To
begin the extensional, {ganai... gi ...} is the standard logical and Lojban "if ..., then ...", which is perfectly serviceable so long as no one tries to win points by pointing out that the antecedent ("if" clause) is in fact false or the consequent ("then" clause) true. When those factors come into play, we have to move to
something other than the present "real world" (the current array of functions or relations assigning individuals to names, classes to properties and so on -- not necessarily the present external world, but the one currently under discussion or presentation), to "possible worlds" (functions -- or relations -- that do as the real world does but perhaps for different individuals and certainly different assignments in some cases). The details of what these other sets of assignments are like is generally irrelevant to using Lojban, we need only know that where we wander can eventually be projected back onto the present world suitably marked as alternative. For the notions we are mainly be concerned with, the only systematic notion that rises to practical importance is that the alternate assignments are "suitably" like the present world -- say, roughly, as realistic as a novel in some genre (which genre says something about how far afield we may
roam). We may also want to specify, in some cases, just how the alternatives are to differ from the present case.
The simplest way to move to an alternate world logically is to postulate, suppose, a situation, which does not hold in the real world (I'll skip the scare quotes). In English we can do this directly, by saying "Suppose/assume that" or the like, or by beginning an obvious tale "Once upon a time, ..." or, rather more complexly, by starting a subjunctive conditional "If I were to...,". The explicit Lojban equivalent of these moves is {da'i}, a free marker that indicates that the current sentence sets up a world and all that follows (down to {da'i nai} or some other convention) is to be about that world. In the casual way, {da'i} is used with {ganai ... gi ...} to make the antecedent the
establishing characteristic and
the consequent the resulting situation (and the {da'inai} is omitted, with some resulting confusion, some times). Note this world specification tends to be rather weak, so specifying not one alternate assignment but many. So arguments can ensue about what happens in the hypothetical case. some are relatively easy arguments to judge: "If I were to relaease this pencil, it would fall" is clearly tied to the present situation and thus assumes the worlds involved differ from the present one mainly in adding that I release the pencil. On the other hand, "If all unicorns were blue, My Pretty Little Uni would be topaz" doesn't have much to hang an argument on (except maybe whether topaz is a shade of blue) and so matters can go on for a while.
Often, however, we are less concerned about what happens in a
particular (sort of)
alternate world as about whether such an alternate world exists at all (within the parameters we have set up in our present assignment for suitable alternate worlds). Something is not the case, but is it possible? That is, in this way of thinking, is there a suitable world in which it does occur? If there is, then it is possible, though not actual. So, we can say, in Lojban {ka'e}. We also have its variants with {na} and {nai}, to say there is not such alternative or the event might not occur or even, combining them, that the event must occur (its non-occurrence is in no suitable alternate world). Occasionally, we want to say something more than that it is possible, but to stress either that it has happened at least once, so may again {pu'i} or that it hasn't yet but still might {nu'o} and {ca'a} which stresses that it is not merely possible but not actual. These three are mainly rhetorical; they add
nothing to the claim of possibility but merely help the argument along, one way or another (the mixture with tense -- another modal notion -- is incidental and generally a bad idea, though there are cases where the mixture makes important points).
Notice that, while I have talked about these features in terms of alternative assignments (possible worlds, etc.), talk in Lojban says nothing about these notions. Statements about possibility could, for all the language shows (until crunchy cases turn up), be just about this world (and, in the official reading of {ka'e}, "innately capable", are. Ignoring this gloss will save a lot of headaches.). Lojban does, for whatever reason, have a direct reference to alternate assignments, in that they can counted off using {mu'ei} with a PA prefix. In this way, {ka'e} has an equivalent in {su'omu'ei} and its dual in {romu'ei}. This also provides an _expression_ for one form of
"probably" without going through {lakne}and for other loose probabilistic expressions. On the whole though, this bringing of worlds from the metalanguage into the object language seems a bad idea. Better to make do the usual notions (some probabilistic terms in CAhA would be nice, though).
That's enough for one round. Note, only modals of truth have been touched on (well, tense, which is also a truth modality, has been mentioned).