1. Speculation & Deduction
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2. MUST Must + infinitive Must have + Past Participle
To say that we are almost sure something is true about the present. (And obligation as well: I must do my homework)
Mary and Tina must be sisters. They look alike.
Must have + Past Participle
To say that we are almost sure something was true or happened in the past.
Titanic must have been an impressive vessel.

3. He can’t be dead. I talked to him 3 minutes ago.
Can’t – couldn’t
Can’t
Can’t/couldn’t + perfect infinitive
To say that we are almost sure that something isn’t true in the present or didn’t happen/wasn’t true in the past.
NOT mustn’t/mustn’t have
He can’t be dead. I talked to him 3 minutes ago.
You can’t/couldn’t have spent very long on this essay – you’ve only written 100 words.

4. May - might - could May/might/could + infinitive
And that means…
TO HAVE + PARTICIPLE
May/might/could + infinitive
May/might/could + perfect infinitive
To say that we think it’s possible that something is true in the present or was true/happened in the past.
I haven’t seen Matt today. He may/might/could be sick.
The keys of the store have disappeared. Do you think someone may/might/could have taken them?
He may/might not have read the message I left on his desk.
Compare:
He might not have done it. (= Maybe he didn’t do it.)
He couldn’t have done it. (= It is impossible that he did it.)

5. SHOULD Should + infinitive (or should have + participle)
To describe a situation you would expect to happen (or would expect to have happened in the past).
If I send the parcel today, it should arrive on Thursday.
I sent the parcel a week ago. It should have arrived by now.

6. Adjectives for speculation
To be bound/sure + infinitive
To express that something is CERTAIN to be true or to happen:
He’s bound to be here in a minute. He left an hour ago.
She is sure to know. She is an expert in the area.
To be likely / unlikely + infinitive
She is likely to recover. Her injuries are not severe.
The company is unlikely to agree to that. They cannot afford paying higher salaries.
It is likely / unlikely + that + clause
I think it is very likely that all of you pass the exam.
It is unlikely that the Government will rise interest rates.

7. Adverbs for speculation
Definitely and probably
They go before a main verb and after the auxiliary (if there is one) in positive sentences and before the auxiliary verb in negative sentences.
She’ll definitely pass the exam. She’s worked hard.
He definitely won’t pass the exam. He hasn’t done any work.
He’ll probably be here at He leaves work at 7.30.
He probably won’t be here until He’s stuck in a traffic jam.
With be they go after the verb in + sentences and before it in – sentences: He’s probably old. The painting definitely isn’t genuine.
! be likely to and will probably are very similar in meaning, but be likely to is more formal:
The new coach is likely to be appointed today.
The new coach will probably be appointed today.