〜はず, 〜べき, 〜ものだ — three different 'shoulds'
English crams three different ideas into one word: 'should'. Japanese splits them cleanly. 〜はず だ is inferred expectation — based on what I know, X should be the case. 〜べき だ is moral / advisable obligation — you ought to do X (it's the right thing). 〜もの だ is general truth or the natural way of things — that's how it is, that's how kids are, that's how life goes. Knowing which one to pick is the difference between 'I think the train should be here by now' (はず), 'You should apologize' (べき), and 'Kids will be kids' (もの).
〜はず だ — inferred expectation
〜はず だ says: based on what I know, X is expected to be the case. The speaker is reasoning from evidence. English: 'should be ~', 'is supposed to ~', 'ought to be ~'. 田中 さん は もう 着いた はず です。 = 'Mr. Tanaka should have arrived already.' (I'm reasoning from his departure time). きょう は 月曜日 だ から、銀行 は 開いて いる はず だ。 = 'It's Monday, so the bank should be open.' Attaches to plain form: verbs and i-adjectives directly (来る はず, おいしい はず), na-adjectives and nouns need な or の (しずか な はず, 学生 の はず). Negative: 〜ない はず. Past: 〜た はず. To say 'should have been but wasn't': 〜はず だった = 'was supposed to ~'. きょう 来る はず だった の に、来なかった。 = 'He was supposed to come today, but didn't.' Don't confuse with 〜わけ だ (last lesson): 〜はず だ is prediction / expectation; 〜わけ だ is conclusion from given facts.
〜べき だ — moral obligation / 'ought to'
〜べき だ says you ought to do something — it's the right or advisable thing. Stronger and more judgment-laden than 〜た ほう が いい ('it'd be better to ~'). English: 'should ~', 'ought to ~', 'must ~ (morally)'. Attaches to dictionary form of verbs: 行く べき, 言う べき, やる べき. Irregular: する → する べき or す べき (formal). 謝る べき だ よ。 = 'You ought to apologize.' 学生 は べんきょう する べき だ。 = 'Students should study.' Negative: 〜べき で は ない = 'shouldn't ~'. うそ を つく べき で は ない。 = 'You shouldn't lie.' Past: 〜べき だった = 'should have ~ed (but didn't)'. もっと 早く 言う べき だった。 = 'I should have said it sooner.' べき has weight — it implies a norm or principle. Don't use it casually for personal preference; use 〜た ほう が いい for that.
〜もの だ — general truth / 'the way things are'
〜もの だ (often 〜もん だ in speech) expresses a general truth, common sense, or the natural way of things. English equivalents are slippery: 'tend to ~', 'will ~ (generally)', '~ is the way of things', 'kids will be kids'. 子供 は 遊ぶ もの だ。 = 'Kids will play (that's what kids do).' 時間 は はやく 過ぎる もの だ。 = 'Time goes by fast (that's how it is).' 人 は だれでも まちがう もの だ。 = 'Everyone makes mistakes (it's human).' Attaches to plain form. Three sub-uses: (1) general truth (above). (2) nostalgia / past habit: 〜た もの だ = 'used to ~ (often)'. 子供 の とき、よく 川 で 泳いだ もの だ。 = 'As a kid, I often used to swim in the river.' (3) mild advice / scolding: 約束 は まもる もの だ よ。 = 'You should keep your promises (that's what one does).' This last use overlaps with 〜べき だ but is softer / more aphoristic — it appeals to common sense rather than imposing a rule.
Choosing between them
Quick decoder. (1) Reasoning from evidence about a specific situation? → 〜はず だ. 電車 は もう 来る はず だ = 'The train should come soon (I checked the schedule).' (2) Telling someone what's right or advisable? → 〜べき だ. 電車 を まつ べき だ = 'You ought to wait for the train.' (3) Stating a general rule of life or how things naturally are? → 〜もの だ. 電車 は おくれる もの だ = 'Trains tend to be late (that's how it goes).' Pitfall: English 'should' for advice is usually 〜た ほう が いい in casual speech, not べき. Save べき for moral / principled cases. Pitfall: 〜もの だ for past habit (〜た もの だ) is nostalgic and a bit literary — it's not the same as 〜て いた ('used to be doing').
〜はず が ない — 'no way' (compare with 〜わけ が ない)
Bonus: 〜はず が ない also exists, meaning 'there's no way (it should be) ~'. 田中 さん が おくれる はず が ない。 = 'There's no way Mr. Tanaka would be late.' Very close to 〜わけ が ない from last lesson. Subtle difference: 〜はず が ない denies based on expectation (it'd be unexpected), 〜わけ が ない denies as logical impossibility (it can't be the case). In practice they overlap heavily. Both colloquially shorten: 〜はず ない, 〜わけ ない.
