Means of expressing modality in Modern English

2.2 The Verb May - Might
This verb means the assumption of possibility of action which can occur, or cannot occur. The verb may in this value can be used both with perfect, and with not perfect infinitive. [ 3.110]
It may rain tomorrow.
Завтра, пожалуй, будет дождь.
I may be away from home tomorrow.
Меня, возможно, не будет завтра дома.
The modal verb may is used for assumption expression in which credibility the speaking is not confident:
1. In combination with Indefinite Infinitive for expressing of assumption related to the present or the future. In this case the verb may is translated into Russian by means of can be, probably, and an infinitive – a verb in the real or future tense. May combination an infinitive can be translated also into Russian by a combination can with an infinitive:
He may not know her address. Он, может быть (возможно), не знает её адреса.
He may come to Moscow in the summer. Он, может быть, приедет в Москву летом.
After the verb may is Continuous Infinitive when it is suggested that the action happens at the moment of the speech: Where is he? - He may be walking in the garden. Где он? - Он, может быть гуляет в саду. For the expression of assumptions may is also used in negative form: He may not know her address. Он, может быть (возможно), не знает её адреса.
You may not find him there. Может быть (возможно), вы не застанете его.

2. 
   In combination with Perfect Infinitive the verb may means the assumption related with any action (or state existence) in the past..
   

May is translated into Russian can be, probably, and an infinitive – a verb in a past tense. The combination of the verb may with Perfect Infinitive can be translated also into Russian by a combination could with an infinitive:
He may have left Moscow. Он, может быть (возможно), уехал из Москвы.
He may have lost your home- address. Он, может быть (возможно), потерял ваш адрес.
It is necessary to pay attention to a compound modal predicate with the verb may in value of the assumption. With a verb in the real or future tense (at not perfect infinitive) or in a past tense (at a perfect infinitive), and this predicate is preceded by the introduction sentence part put into words by "can be", "probably", and in case of an interrogative sentence – it is "interesting". [3,127]
It is interesting to note that the verb may in value of assumption is very widespread both in art, and in scientific literature.
Linguist K. N. Kachalova writes about the use of the modal verb might that it is used for expression in the indirect speech depending on a verb in a past tense:

1. 
   In combination with Indefinite Infinitive when in the corresponding direct speech it would be necessary to use may with Indefinite Infinitive:
   

He said that she might know their address.
Он сказал, что она, возможно, знает их адреса.

2. 
   In combination with Perfect Infinitive when in the corresponding direct speech it would be necessary to use may with Perfect Infinitive :
   

He said that she might have lost their address.
Professor L.S. Barkhudarov about use of the might form writes that in combination with a perfect form of an infinitive might expresses a guess, and also the assumption with big degree of uncertainty and doubt ("who knows").
“I don`t know how long the silence lasted. It might have been for half and hour.”
The combination of might to a perfect form of an infinitive can express also alleged action which implementation is obviously impossible.
“Had she been fourteen instead of twenty-four, she might have been changed by then (but she was twenty-four, conservative by nature and upbringing). It is necessary to notice that the might form in value of assumption is used mainly in affirmative offers. If after might there is a denial, it belongs not to the assumption, and to action (or to a state), expressed by an infinitive. [3, 134]
To compound modal predicate with might in value of the assumption contradicting reality, there corresponds in Russian the simple or compound (not modal) predicate expressed by a verb in the real or past tense (depending on an infinitive form), and the sentence with such predicate is entered by the words "as though", "it (would) be possible to think", "it is possible to think that …".
Historically verbs should and ought to were two forms of one verb, expressing a duty. But with the language development they began to designate various values and in the modern language these verbs are already used separately and they are considered as two separate verbs. Similar to other modal verbs, the verb should loses the value of desirability and, except value of a duty, also designates the assumption.
It should be about five now.
Сейчас, должно быть, около пяти часов.
Use of the verb should in this value practically is not described. I.P. Krylova only specifies that the verb should is not so often used in this value and, as a rule, value of the assumption is transferred by the verb must.
The verb ought to is used similarly, expressing caused, based on certain circumstances, probability. [ 4,69]
Ought to loses the initial value and also expresses the assumption.
The combination of verbs should and ought to not perfect infinitive indicates simultaneity of the assumption and alleged action (or states), a combination to a perfect infinitive – precedence of alleged action suggested.
It should be noted that verbs should and ought to are interchangeable. If he started at nine he ought to be (should be) here by four.
Если он отправился в девять, ему бы следовало быть здесь к четырём часам. They left at nine, so they ought to (should) have arrived by now.
Они уехали в девять, следовательно, сейчас им бы следовало уже приехать. The author is a well-known expert, so his book ought to be (should be) reliable.
Автор является известным специалистом, поэтому на его книгу, вероятно, можно положиться.
That should (ought to) please you.
Это, вероятно (должно быть) доставит вам удовольствие.
Verbs should and ought to in value of assumption can be used not only in affirmative, but also the negative sentence, and denial belongs not to the assumption, and to action (or to a state), expressed by an infinitive:
It ought not to be very hard to find a man who is prepared to come and talk German to me for an hour. – «Вероятно, не очень трудно найти человека…» I.P. Krylova notes that in value of the assumption the verb ought is used, not really often as in this value it is usually replaced with verb must. However, there are some set expressions with a verb ought to:
He/you ought to know it (=he is/ you are supposed to know it).
You ought to be ashamed of yourself.