Hi friends,

I need your help on the following. I don't think my English is all that bad, but I frequently get confused when trying to use the following verbs. A detailed description with examples is as follows:

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may
might
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May I come in?
Might I come in?

She may do it / She may not do it.
She might do it / She might not do it.

She may have done it / She may not have done it.
She might have done it / She might not have done it.

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can
could
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Can I take you for dinner?
Could I take you for dinner?

He can do it / He can't do it.
He could do it / He couldn't do it.

He can have done it / He can't have done it.
He could have done it / He couldn't have done it.

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shall
should
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Shall we meet after lunch today?
Should we meet after lunch today?

She shall do it / She shall not do it.
She should do it / She should not do it.

She shall have done it / She shall not have done it.
She should have done it / She should not have done it.

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must
have to
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Must I assemble here?
Do I have to assemble here?
Have I to assemble here? (Haven't used this construct anytime in my life, not even sure if this is grammatically correct)

He must do it / He must not do it.
He has to do it / He doesn't have to do it.

He must have done it / He must not have done it.
He has have to do it (?) / He hasn't have to do it (?)

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will
would
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Will you get me the check, please?
Would you get me the check, please?

She will do it / She will not do it.
She would do it / She would not do it.

She will have done it / She will not have done it.
She would have done it / She would not have done it.

Thanks!!
She shall do it / She shall not do it. ONLY USED FOR THREATS AND PROMISES.
She shall have done it / She shall not have done it. ONLY USED FOR THREATS AND PROMISES.
Have I to assemble here? YES, THIS IS FINE, IF RATHER FORMAL.
He has had to do it / He hasn't had to do it.

All the other sentences are fine, Ezfred.
Can I take you for dinner ? Capacity or permission
Could I take you for dinner, if you were not sick ? Could is hypothetical

He can do it : he has the power to, the capacity
He could do it : under certain circonstences

Shall we meet : Will we meet (it is sure that we meet, or do we want to meet )
Should we meet : Do we have the duty to meet

He must : obligation, no choice
He has to : still a choice
He must not do it : no choice
He doesn’t have to do it : he doesn’t need to, doesn’t matter

He will do it if I ask : hypothetical futur
He would do it if had asked. : hypothetical present
Would you please get me the check : the check which is in your hand, would you gice it to me now ?
Willy ou give me the check, please : One day or an another, in the future, will you give me the check.
She will have done it by the end of the week, sure
She would have done it (would be already done if…)
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Modality in English is a complex topic. You might want to start with this, which just scratches the surface.

The modal expressions of English fall into two major groups, the modals of logic and the modals of interpersonal volition. Each of these groups can be subdivided according to a property we may call "constraint", which when "unconstrained" relates to possibilities (in the world of logic) and freedom to act (in the social world), and when "constrained" relates to what is necessarily so (logically) and to lack of freedom to act (in the social world). The possibility of "weakly constrained" modality also exists. It relates to what is probably so (logically) and to what is advisable (in the social world).

Unconstrained modals of logic have to do with logical possibility.
Constrained modals of logic have to do with logical necessity.
Weakly constrained modals of logic have to do with logical expectation.

Unconstrained modals of interpersonal volition have to do with permission.
Constrained modals of interpersonal volition have to do with obligation.
Weakly constrained modals of interpersonal volition have to do with advisability.

Each of the six classes described exists in two polarities.

For logical possibility (unconstrained), we may speak of the possibility that a certain situation exists as well as of the possibility that a certain situation does not exist. The most representative words for these concepts are might and might not. Alternates for might are may and could. An alternate for might not is may not.

For logical necessity (constrained), we may speak of a situation that necessarily exists as well as of a situation that necessarily does not exist. The most representative words for these concepts are must and must not. An alternate for must not is can't.

For logical expectation (weakly constrained), we may speak of a situation that is expected to exist as well as of a situation that is not expected to exist. The most representative words for these concepts are should and should not. An alternate for should is ought to; an alternate for should not is ought not.

For interpersonal modality, we may speak of granting permission (unconstrained) and of denying permission (constrained) to perform certain acts. The most representative words for these concepts are can and can't. An alternate for can (indeed, the preferred expression according to traditional grammars) is may. Alternates for can't are may not (also traditionally preferred) and must not.

For interpersonal modality, we may speak of situations where it is imperative (constrained) that some act be performed as well as of situations where it is not imperative (unconstrained). The most representative words for these concepts are have to and not have to. (These are considered semi-modals grammatically.) An alternate for have to is must. need to also sometimes serves in this role. A less used alternate for not have to is needn't.

For interpersonal modality, we may speak of situations where it is advisable (weakly constrained) that some act be performed as well as of situations where it is not advisable that an act be performed (or advisable that it not be performed) (weakly unconstrained). The most representative words for these concepts are should and should not. (These are more frequently used for interpersonal modality than for logical modality.) As above, alternates are ought to and ought not.

will and would are used to form the future (of the present) and the conditional (or future of the past), respectively, and do not enter into the network of relationships described above.

can and could are used to denote physical or mental abilities in addition to the uses described above.