The 助動詞（じょどうし） (auxiliary verb)
まい is used in Japanese to express negative volition. This means that in many ways, it is the opposite of う and よう, which are the auxiliary verbs that express positive volition.
まい connects to the base form of verbs, and is considered slightly formal.
まい may be translated as ‘won’t (A)’, ‘to intend not to (A)’, or ‘probably not (A)’. It can be considered as a condensed way of expressing ～ないだろう.
-
あんな接客（せっきゃく）が雑（ざつ）なレストランにはもう行（い）くまい。
I probably won’t go back to that restaurant with such poor customer service.
あのアパートの家賃（やちん）は高（たか）いので、あそこには住（す）むまい。
The rent for that apartment is expensive, so I probably won’t live there.
Caution - When appearing with する or 来（く）る, it is also common to see
まい connected to the 連用形（れんようけい） (masu-stem conjunctive form) as
しまい,
すまい,
きまい and
こまい. However, the standard
するまい and
来（く）るまい are also quite common structures.
-
田中（たなか）くんはとてもいい人なので、そんなひどい事（こと）はしまい。
Since Tanaka-kun is a nice person, he probably wouldn’t do such a terrible thing.
台風（たいふう）の警報（けいほう）が出（で）ているので、今日（きょう）中（じゅう）に届（とど）くはずだった荷物（にもつ）はこまい。
Since there was a warning announced for the typhoon, I probably won’t get the package that I was expecting today.