English modals

Modals: A modal verb (also modal, modal auxiliary verb, modal auxiliary) is a type of auxiliary verb that is used to indicate modality. The use of auxiliary verbs to express modality is a characteristic of Germanic languages.
In the English language, a modal verb is an auxiliary verb that can be used to change the grammatical mood of a sentence. The key way to identify a modal verb is by itsdefectiveness (they have neither participles nor infinitives).

The modal verbs in English are as follows, paired as present and preterite forms:
• shall and should
• will and would
• may and might
• can and could
• mote (Archaic) and must
The following are not modal verbs but may be used for a similar purpose:
• ought to and had better
• used to
• dare andneed
• do
• going to
• have to

Shall and Will Shall is used in many of the same senses as will, though not all dialects use shall productively, and those that use both shall and will generally draw a distinction (though different dialects tend to draw different distinctions). In standard, perhaps old-fashioned English, shall in the first person, singular or plural, indicatesmere futurity, but in other persons shows an order, command or prophecy: "Cinderella, you shall go to the ball!" It is, therefore, impossible to make shall questions in these persons. Shall we? makes sense, shall you? does not.
Shall derives from a main verb meaning to owe, and in dialects that use both shall and will, it is often used in instances where an obligation, rather than an intention, isexpressed.
Shall is also used in legal and engineering language to write firm laws and specifications as in these examples: "Those convicted of violating this law shall be imprisoned for a term of not less than three years nor more than seven years," and "The electronics assembly shall be able to operate within its specifications over a temperature range of 0 degrees Celsius to 70 degreesCelsius."

Should : is commonly used, even in dialects where shall is not. The negation is "should not" (or the contraction "shouldn't").
Should can describe an ideal behaviour or occurrence and imparts a normative meaning to the sentence; for example, "You should never lie" means roughly, "If you always behaved perfectly, you would never lie"; and "If this works, you should not feel a thing" meansroughly, "I hope this will work. If it does, you will not feel a thing." In dialects that use shall commonly, however, this restriction does not apply; for example, a speaker of such a dialect might say, "If I failed that test, I think I should cry," meaning the same thing as, "If I failed that test, I think I would cry."
In some dialects, it is common to form the subjunctive mood by using should:"It is important that the law should be passed" (where other dialects would say, "It is important that the law be passed") or "If it should happen, we are prepared for it" (or "Should it happen, we are prepared for it"; where early Modern English would say, "If it happen, we are prepared for it," and many dialects of today would say, "If it happens, we are prepared for it").

May and might: donot have common negative contractions (equivalents to shan't, won't, can't, couldn't etc.), although mightn't can occur in asking questions. ("Mightn't I come in if I took my muddy boots off?" as a reply to "Don't come in here! You'll get the floor dirty!")
Both forms can be used to express a present time possibility or uncertainty ("That may be."). Might and could can also be used in this sensewith no past time meaning. Might and may would carry the same meaning in "John is not in the office today, and he could be sick."
May is also used to express irrelevance in spite of certain or likely truth: "He may be taller than I am, but he is certainly not stronger" may mean roughly, "While it is true that he is taller than I am, that does not make a difference, as he is certainly not...