Logical Assumptions/Deductions
Must, may, can't, etc+bare infinitive : for assumptions about the present. Perfect infinitive: for assumptions about the past.
Must = almost certain that this is/was true. She's been working all day, so she must be really tired!
She was working all day yesterday, so she must have been really tired!
May/Might/Could = possible that this is/was true.
John isn't at work today - he may/might be out of town on business.
John wasn't at work yesterday - he may/might have been out of town on business.
Can't/couldn't = almost certain that this is/was impossible
That can't be Janet over there - she's at her grandparents at the moment.
That can't have been Janet you saw - she was at her grandparents ' at that time.
Note how the tenses of the infinitive are formed :
Present simple : (to)cook
Present continuous: (to)be cooking
Present perfect simple: (to)have cooked
Present perfect continuous:(to)have been cooking