‘ala’ plays at least five separate, but interrelated, roles in toki pona, all somehow called negation and, in true toki pona fashion, none clearly distinguished from the others in the vocabulary or the grammar (and often in the context even). This gives rise to several problems which require solutions, usually by fiat.
As a logician, I tend to focus on the logical uses, sentential negation and negative quantifiers. Sentential negation is just a function that converts a sentence into its negation, a sentence false when the first was true, true when the first as false, “It is not the case that…”. In simple English sentences this is expressed by “not” right after the main verb, in more complicated cases, it gets (of course) more complicated, but logicians tend to solve that by pulling “It is not the case that” out in front of all the complications. toki pona does not have this device available (the suggestion to use ‘ala la’ for it is regularly rejected as being unpona or even lojbanish, which it is, of course). The result is that either we have to do a lot of internal adjustments to get the right results or we have to avoid saying things like that altogether. The latter seems easier and we will discuss those directly. For now, sticking to simple sentence, we can think (incorrectly, it turns out) of sentential negation as ‘ala’ immediately after the predicate head, “verb”.
The negative quantifier “no” is just ‘ala’ modifying whatever word specifies the sort to thing not involved. This creates an amusing conflict with a later use of ‘ala’, to specify the complement class, since ‘jan ala li kama’ can mean “A non-human came” as well as “Nobody came”. To be sure, the “non-human” reading is usually implausible, but the trap is always there. In logic, “nobody” is just “not somebody”, with a sentential “not” ranging over a particular quantifier, “some”. Since toki pona does not have an explicit “some”, this interpretation is not quite possible, since ‘jan li kama ala’ will (as we will see) get read as “Somebody did not come”, even though we just said (albeit with disclaimers) that ‘kama ala’ ought to be a sentential negation. These sorts of problems are not just with “some”, but with all the explicit quantifiers, “ali” and numbers and even ‘ala’, itself.
To see how this plays out, we turn to the third sort of negation that ‘ala’ represents, indeed, to the one that is sometimes listed as its only meaning: complementation. If a word, w, refers to a class of things or members of that class, then ‘w ala’ refers to the class of everything not in the first class, for whatever reason. So, ‘loje’ refers to the class of all red things and ‘loje ala’ refers to everything else: green things, blue things, ideas, irrational numbers, running, spirituality, etc. So long as the answer to the question is “Is it red?” is “No”, it is in the class referred to by ‘loje ala’. But while this works for individual things, it works less well for general expressions: if some particular thing is in the complement of ‘loje’, then that thing is not in ‘loje’. But, of course, the mere fact that something or other is not in loje doesn’t mean that something or other else may not be in ‘loje’. So, ‘ala’ on the verb works fine as a sentential negation as long as not quantifiers are involved, but it is not always obvious when quantifiers are involved. Further it is not decisively settled what to do when quantifiers are involved. Cases of quantifier plus negation always present two possibilities and it is not clear which is the normative one and, given an answer to that, how to give the other possibility.
It may be illuminating to see what happens with Y/N questions under the two possible readings. Consider “Did everybody come?”, naturally translated as ‘jan ali li kama ala kama?’. Since this is covertly a choice question between ‘jan ali li kama ala’ and ‘jan ali li kama’, there are four possible answers: ‘(kama) ala’, ‘kama’, ‘ala tu’ (“neither”) and ‘tu ali’ (both) which can’t apply in this case (but see later). ‘tu ali’ is also assumed not to apply in this case, but does on some interpretations. So, suppose everybody comes. The ‘jan ali li kama’ is true on either interpretation and is the right answer. Suppose that no one comes. Then ‘jan ali li kama ala’ is true on the complement interpretation, since every person is in the class of non-comers. It is also true on the sentential reading, since ‘jan ali li kama’ is disconfirmed in the extreme. The stronger claim, that nobody came, might be more informative, but the weaker is still true and may be adequate. But what if some came and others did not? Both claims are now false on the complementary, not everybody is in either the class or its complement but some are in each. So, only the “neither” (‘ala tu’) response is correct (despite not being offered as a choice officially). In the sentential reading, however, only the unnegated form is false, for not all are in the class. To be sure, it might be useful to know that only some are in the class, but that is not necessary for the given question (filling this gap is one of many uses of the ‘anu seme?’ question). A similar pattern (though reversed) arises with “Did anybody (somebody) come?” ‘jan li kama ala kama’ (with ‘jan’ somehow despecified). Cleary. if everybody came, the ‘kama’ answer is true and the ‘kama ala’ false. Similarly, the reverse holds if nobody came, though in both cases, additional information might be given. But when some came and some didn’t, the complement interpretation should strictly answer ‘tu ali’, some things are in the base class and some things in the complement. But in the spirit (if not the letter) of Y/N questions, just the ‘kama’ is required. That is, of course, the correct answer for the sentential reading, since “it is not the case that somebody came” is false. Hopefully these cases help to choose what to say under a given interpretation. While it doesn’t ultimately matter which one you choose, pu seems to hold to the complement interpretation and that is assumed from now on.
The other two negations are simpler in outcome, though sometimes harder to explain. One of these is the notion of a polar opposite. This is a subclass of the complement class which contains the things most different from the regular class (usually, admittedly, within some broader class, that is, being a totally different sort of thing -- an object and action, for example -- doesn’t enter, just one object and another). The idea seems very subjective. If you have a color wheel in mind, the the polar opposite of red is green , but that makes no sense in a linear spectrum. But there are many cases where culture at least sets out obvious cases, good and bad, dark and light, living and dead, and so on through manny adjectives. Nouns and verbs are more problematic although, for some verbs at least, the is the notion of undoing from doing: regurgitation from ingestion, taking from giving, writing and erasing, and so on. The point is that, where the opposite is not separately given a word, ‘ala’ can be pressed into service for the notion. It is not clear how to tell when this happens without some considerable surrounding talk, but it is a legitimate move.
The final negation is of presuppositions. This is called into play when something is said that presupposes something else that is not established. The classic is the loaded question ‘sina pina ala pini utala e meli sina?’, say. Either ordinary answer is an admission that you have beaten your wife. Fortunately, in tp the answer ‘ala tu’ “neither” is legitimate and gets out of that (though someone may try to contest the dodge). There are many contemporary examples of another class type “Why hasn’t Hillary been imprisoned for her treasonous activities?” Which officially only allows an answer of the form “The reason is …” aad not of the form “There have been no adjudged treasonable activities to prosecute, let alone imprison for” and so on. One response is just to say that there are presuppositions here that need to be dealt with before the question as presented can be answered. Various forms of “super ‘ala’” have been dreamed of for this purpose but none has been established as a shortcut for the long version above. But one might come in handy if we ever get around to doing debates in tp.