Sometimes my life in logical languages attacks me in the midst of the toki pona world. Several occasions recently have come together in this.
Consider 'jan ali li kama ala' "Everybody didn't come". Ordinarily we take 'ala' coming right after the verb (the first word after 'li') to mean the negation of the whole remaining sentence. So, this is the denial of 'jan ali li kama', "Everybody came". Of course, another way of saying that is "Not everybody came" 'jan pi ali ala li kama' And yet a third way is "Somebody didn't come" which is apparently 'jan li kama ala'. But now, we have a problem, since this looks to be the negation of 'jan li kama' "Somebody came" and so the same as 'jan ala li kama' "Nobody came". And that, in turn, is another way that people read "Everybody didn't come" and probably 'jan ali li kama ala': in logiquese "Every person is such that they did not come"
So, the problem is that 'ala' (like 'kin' and 'taso' and maybe a couple other words) can attach to just about anything in a sentence is a possibly meaningful way. At that slot just after the verb (though not elsewhere?) it negates the whole sentence. But it can also be used to "negate" just the immediately preceding word (or, elsewhere, finished phrase), either complementing it (making it assert something other than what the word or phrase originally meant) or opposing it (making it assert the exact opposite), So, assuming that our original claim, that the 'ala' in 'jan ali li kama ala' was a sentential negation, when we get to 'jan li kama ala', the 'ala now is merely negating 'kama', not the whole sentence. And it is this reading which then makes 'jan ali li kama ala' mean "Nobody came", Even the usual grammar does not help in this case, since '(kama ala) appears in either case and there is no good internal reason for suggesting different transformational histories for the two cases. To be sure, in a total Montagovian grammar the underlying formulae would be different, but those niceties were lost long before anything visibly tp was in hand. For a rather extreme example, nothing that might naturally develop into 'ala la jan ali li kama' has any support in the language (I suppose something like "It is not the case that everybody came").
Problems similar to those with "all" and "some" arise with "and" and "or", of course. Does 'ona li alasa ala e waso e soweli' means that he hunts neither or just not both? And similarly for 'ona li alasa ala e waso anu soweli'. It would seem that we have to take both these as fusions of negated sentences, since we have no grammatical process for introducing negation after fusion, only in simple sentences (and rather obscurely even there). Thus, the conjoint cases means that he hunts neither birds nor beasts, since it is from 'ona li alasa ala e waso. ona li alasa ala e soweli'. The disjoint case then says only that he doesn't hunt both, coming from 'ona li alasa ala e waso, anu ona li alasa ala e soweli'. Note that the effect here (aside from basic DeMorgan changes) is to make the two sentential negations into a single predicate negtion. The only (easy) way to get the corresponding sentential negation is exactly the DeMorgan route, using the conjunction for the disjunction and conversely.
These puzzles (calling them problems is the logician talking) arise primarily from the rule that would take the 'ala' after the verb as a sentential negation. If all 'ala' modified only the preceding phrase, the puzzles would disappear. It would, however, mean that new expressions would have to be found for the old sentential negations involving quantifiers (including numbers) and maybe some other complex cases. In some cases, like the negation of 'jan ali li kama', such expressions are readily at hand ('jan ali ala li kama') and maybe they are for all cases (though 'jan tu wan ala li kama' as a denial of 'jan tu wan li kama' looks odd). Alternately, we might consider whether 'ala la' "it is not the case that" might be a reasonable tp expression, at least in some very fussbudgetal contexts. It is just not clear how backwards compatible such a move would be, but I suspect that there would be few problems, since the hard cases feel hard at the start and would usually be avoided. And it does simplify the grammar a bit.
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