Negatives follow the verb, noun or preposition it modifies.
Tacking “ala” should create polar opposites like “mal” in Esperanto, but doesn’t always. Just as with words in the positive, “ala” could negate any quality of the noun.
Here is an example of putting the negative after the auxiliary verb.
- “sina ken ala tawa kepeken nasin ni.”– jan Pije
- [you] [omit verb marker] [aux verb:able] [not] [verb: go] [Prep: with/using] [road] [this]
- You are not able to go on this road.
Here is an example from the same page showing how the negative is used to ask a question expecting one of two opposite responses (i.e. a yes/no question)
- “sina wile ala wile kama?”
- [you]  [verb:want] [not] [verb:want] [to come]
- Do you want to come?
Negatives for prepositions.
When I first read this, I thought ala modified the preposition. Then I saw the “e” and thought “kepeken” must be modifying the verb and “ala” modifies “lon kepeken”
- ? “nasin pi lawa ala la jan li lon kepeken ala e jan lawa.” http://tokipona.wikia.com/wiki/nasin_pi_lawa_ala
- the way of no-leader is where people do not co-exist-with the leader
I don’t know if this is legal, but if it was, there would be six more prepositions in the language,kepeken ala being the easiest to translate into English as without.
- “nasin pi lawa ala la jan li lon kepeken ala jan lawa.”
- the way of no leader is where people exist without a leader.