"Should" in Japanese

Question

The word "should" in English has these uses when not used as a question:

1. To express the expectation of the speaker (Probabilistic reasoning).
   • The train should arrive in 10 minutes.
2. To express a condition
   • Should it rain, the event will be cancelled.
3. To express obligation or the duty of ~.
   • I should go home.
   • You should study hard for the exam.
4. To indicate an ideal state perceived by the speaker.
   
   • Everyone should have equal rights.

From my understanding, I use ~はず for 1., ~ば(or other conditionals) for 2., and ~べき for 3. .

(Question) What can I use for 4.?

Answer 1

2 could also use 場合 to be a little more formal (雨の場合は...). 3 can also use ～もの as another option to ～べき (猛勉強するものだよ！).

4 lacks a little context. While most of the time it will be perceived as subjective (i.e., "(It's my opinion that) Everyone should have equal rights," it could also be objective in a few circumstances. For example, "A new law passed. Therefore, everyone should have equal rights (now)," or something similar. Each case would use something different, and I'm thinking ～べき again if it's subjective and ～はず if it's objective.

I'd also add a #5 to your list: subjective recommendation, for which you could use 〜たほうがいい (and, I believe, also 〜たらいい or 〜ばいい).

お前、風邪【≪かぜ≫】気味【ぎ・み】だね。今日学校を休んだほうがいい。　→　You seem sick. You should stay home from school today.

Answer 2

TL;DR You should be able to use ～はず or ～べき to indicate an ideal state perceived by the speaker, but a phrase that contains 理想 would help to emphasize that fact.

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1. To express the expectation of the speaker (Probabilistic reasoning)

You say that you would use はず in this case, but given your sample sentence that sounds a bit too strong (unless you are really trying to emphasize the point). I think that ～だろう／～でしょう or even ～よう would be perfectly acceptable and probably more common.

"The train should arrive in 10 minutes."

電車はあと十分で来るでしょう。 (when you are expressing your belief or opinion)

電車はあと十分で来るようです。 (after looking at a timetable)

2. To express a condition

I agree with you in saying that ～ば (or some other conditional) would be appropriate in this case.

"Should it rain, the event will be cancelled."

雨が降ったらイベントは中止になります。

3. To express obligation or the duty of ~

You say that you would use ～べき in this case, but the following would also work just as well.

• ～なければならい
• ～なければいけない
• ～ないといけない

In fact, I think that these are used more often than ～べき.

"I should go home."

家に帰らなければいけない。

"You should study hard for the exam."

ちゃんと勉強しないといけないよ。

Note that you can also use こと to express obligations (I often see this in bulleted lists).

"You should study every day."

毎日勉強すること。

4. To indicate an ideal state perceived by the speaker

Here I think that you could use either ～はず or ～べき, but to make it clear that you're talking about an ideal state it would probably help to start your sentence with a phrase containing 理想.

"Everyone should have equal rights."

理想上では皆に平等の人権があるはず。