Modal auxiliary verbs can express ability, obligation, permission, and request. They can also express probability, or how certain a situation is.
Must = logically probable. Can't = logically impossible.
He must be exhausted. He hasn't slept for 24 hours!Sue can't have a ten-year-old daughter! She's only 24!Aren't they answering? They must be in bed.The continuous infinitive is formed with be + -ing.
You must be joking! They can't still be eating! Peter might be working late.Question forms with modal verbs of probability (e.g. Might she be … ?) are unusual. We usually use Do you think … ?
Do you think she's married? — 'She can't be.'Where do you think he's from? — 'He might be Portuguese.'The perfect infinitive (have + past participle) is used for probability in the past.
He must have caught a later train.They might have lost our phone number.| Modal | Meaning | Example |
|---|---|---|
| must have | almost certain (logical deduction) | He must have been exhausted. |
| can't have | logically impossible | She can't have told him about us yet. |
| may/might have | possible (uncertain) | The letter may have got lost. |
| could have | possible (less definite) | He might have changed his mind. |
The continuous perfect infinitive is formed with have + been + -ing.
She must have been joking. They can't have been trying very hard.