Explanation
Exercises
Past Deduction with Modals
must have • can’t/couldn’t have • may/might/could have • should/ought to have

Quick certainty map (past)

ModalCertaintyMeaningFormExample
must have 90–100% sure TRUE strong logical conclusion must have + past participle The lights were on. They must have left in a hurry.
can’t / couldn’t have 90–100% sure NOT true strong negative conclusion can’t/couldn’t have + past participle He was abroad. He can’t have attended the meeting.
may / might / could have 30–60% possible speculation (we don’t know) may/might/could have + past participle The email might have gone to spam.
should / ought to have expected past expectation/criticism should/ought to have + past participle You should have told me earlier.

Use these forms to talk about past situations only. For the present use: must be / can’t be / may be, etc.

must have + V3 — strong positive deduction

  • Logic evidence points strongly to a past fact.
  • They didn’t answer— they must have been asleep.
  • Judging by the footprints, a fox must have crossed the yard.

In negative deduction, use can’t/couldn’t, not *mustn’t (which means “not allowed”).

can’t / couldn’t have + V3 — strong negative deduction

  • Almost certain it didn’t happen
  • Her flight landed at 9. She can’t have arrived at 8.
  • That voice couldn’t have been the manager. He’s away.

may / might / could have + V3 — possibility in the past

  • Neutral/uncertain She may have missed the train.
  • Negative possibility use may/might not have (not *could not for this meaning): They might not have heard you.
  • Unrealized ability/opportunity with could have: You could have called, but you didn’t.

should / ought to have + V3 — expectation & criticism

  • Expected but didn’t happen We should have left earlier.
  • Polite criticism He ought to have checked the figures.
  • Negative You shouldn’t have shouted. It was rude.

Ought to is slightly more formal/less common than should; both take to have + V3 in the past.

Form & word order

AffirmativeNegativeQuestionsPassive
subject + modal + have + V3
She must have forgotten.		 modal + not + have + V3
He might not have seen it.		 modal + subject + have + V3?
Could they have left early?		 modal + have + been + V3
The file may have been deleted.

Present vs past deduction (compare)

  • Present He must be at work. / He can’t be at home.
  • Past He must have been at work. / He can’t have been at home.

For continuous past actions, use been + V-ing: They must have been waiting for hours.

Common pitfalls

  • ❌ He mustn’t have arrived (means “it’s not allowed”) → ✔ He can’t have arrived.
  • Don’t mix couldn’t have (strong negative deduction) with might not have (weak negative possibility).
  • Use the past participle after have: ✔ must have gone, ✖ must have went.
Exercises:
1
2
3

Past Deduction with Modals

Choose the correct option for each gap below.
1
The alarm wasn’t set and the lights were on — I’m sure they forgotten to lock up.
2
The streets are completely dry — it rained last night.
3
I found Marta’s umbrella on the sofa — she dropped by while we were out.
4
Our inbox is empty — you sent the email yet.
5
I didn’t see your message earlier; it been filtered into spam.
6
The museum closed at 6 p.m., so they taken those photos inside at 7.
7
There’s paint on your sleeves — you painting the fence this morning.
8
No one answered the phone; they gone to the cinema.
9
Your fitness app shows zero steps — you walked to work this morning.
10
The parcel is on the porch — the courier delivered it while we were out.

Past Deduction with Modals

Choose the correct option to complete the sentences below.
1
His office is dark and his car isn’t in the lot. He ______ left already.
A.
B.
C.
D.
2
It was 2 a.m. and nobody answered the phone. They ______ been asleep.
A.
B.
C.
D.
3
The street is wet but the sky is clear now. It ______ rained earlier.
A.
B.
C.
D.
4
You paid double for the ticket. You ______ checked the price first.
A.
B.
C.
D.
5
She looked genuinely surprised. She ______ known about the party.
A.
B.
C.
D.
6
The door was locked from the inside. They ______ left the house yet.
A.
B.
C.
D.
7
He won the marathon again. He ______ trained incredibly hard.
A.
B.
C.
D.
8
I saw the lights on all night. He ______ been working late again.
A.
B.
C.
D.
9
All the cookies are gone. The kids ______ eaten them after school.
A.
B.
C.
D.
10
I heard a bang outside. It ______ been the wind slamming the gate.
A.
B.
C.
D.

Past Deduction with Modals

Complete the sentences using the verbs in brackets with a past modal verb form.