modal verbs of deduction

Question

¡Hola!
Could you please provide me with Spanish equivalents for modal structures of probabality:
-Must/might/may/could + be (+ V-ing);
past probabality:
-Must have/might have/may have/could have + past participle (+ V-ing);
and their negative forms
Thanks in advance
Regards,
Alexander

Accepted Answer

Hola Alexander
To express probability in the present (progressive) we generally use:
-Debe estar ( + gerundio)
-Debe de estar ( + gerundio)
-Podría estar ( + gerundio)
-Puede que esté ( + gerundio)
for must/might/may/could + be (+ ing)
To express probability in the past (progressive) we generally use:
-Debe haber estado ( + gerundio)
-Debe de haber estado ( + gerundio)
-Podría haber estado ( + gerundio)
-Puede que haya estado ( + gerundio)
for must/might/may/could + have been (+ ing)
To negate all these above, the most natural way would be placing "no" before the modal in the case of "deber", so:
-No debe estar (-ing)
-No debe de haber estado (-ing)
but after the modal with poder:
-Podría no estar (-ing)
-Podría no haber estado (-ing)
However with "puede que" it must be after "que":
-Puede que no esté (-ing)
-Puede que no haya estado (-ing)
I hope this helps.
We are still working on some advance lessons on modals. The progressive aspect has just been noted to include in our content.
Saludos
Inma

Answer

¡Hola Inma! 
Muchas gracias por su respuesta))
Could you be so kind to answer some more questions?
a) What's the difference between
debe + infinitivo/infinitivo compuesto/estar+gerundio/haber estado + gerundio
&
debe DE + infinitivo/infinitivo compuesto/estar+gerundio/haber estado + gerundio?
Namely, does the preposition "DE" make any difference?
b) What are the equivalents for can't & must not for logical conclusions in Spanish?
For example:
(present)
The restaurant can't be open - the door is locked
The restaurant must not be any good - it is always empty
(Past)
He had left the office at 6:00 p.m. He can't /couldn't have been at home at 6:05 p.m
She was not answering the doorbell. She must not have been at home then.
How can I express this difference in Spanish?
c) Is it possible to use debería/podría haber + participio in Spanish like could/may/might have + past participle in English - for both expressing regrets about something that was not done in the past / criticizing someone for not doing smth
& for making suggestions about possible completed events?
d)Is no tenía que haber+participio an equivalent for needn't have (done)? 
Regards,
Alexander