Auxiliary verbs

• Be

• Can

• Do

• Have

• May

• Must

• Ought

• Shall

• Will

Modal auxiliaries broad categories

• Possibility/Permission

• Necessity/Obligation

Modal auxiliary verbs

Modal Auxiliary	Present Neutral	Present Negative	Past Neutral	Past Negative
can	can	cannot / can’t	could	could not / couldn’t
may	may	may not	might	might not
must	must	must not / mustn’t	— (no true past form)	—
shall	shall	shall not / shan’t	should	should not / shouldn’t
will	will	will not / won’t	would	would not / wouldn’t
ought	ought (to)	ought not (to)	— (no distinct past form)	—
need (modal use)	need	need not / needn’t	—	—
dare (modal use)	dare	dare not / daren’t	—	—

Note: Modals have only present and past tense, no participles, no plain form

Shall is used, but rarer.

Would reflects remoteness

May is often used to describe something as possibly true in the sense of being compatible with everything we know

There may be no integer solution to this equation

Modality

Modality	Meaning	Example sentence
Ability	Subject has the capacity to do something, freedom to do something	She can swim.
Possibility	Something is possible but not certain	She may arrive later.
Probability	Speaker judges something as likely	He should be home by now.
Prediction	Speaker predicts a future situation	They will win the match.
Firm Prediction	Firm prediction	We shall overcome.
Soften Prediction	Not as past, but reduced assertion	We should be all right.
Permission	Allowing someone to do something	You may leave early. You can go now. Can I kiss you? You may kiss me now.
Obligation	Something is required	You must wear a helmet.
Moral or Ethical Obligation	Duty or obligation	You ought to be careful. You should be more careful (here should is another lexeme, not past of shall)
Determinism, no choice	inner determination, commanding	You will do as I say. I will get this done

| Prohibition | Something is not allowed | You must not park here. | | Advice | Speaker recommends something | You should see a doctor. | | Volition / Willingness | Subject is willing or determined | I will help you. | | Necessity | Something is logically required | This must be the place. You needn’t wear shoes | | Epistemic Necessity (logic inference) | Strong logical inference, based on evidence | There must be something wrong with mechanism |

Common uses of should

Use	Example
Advice	You should see a doctor.
Weak obligation	Students should submit the form today.
Expectation / probability	The train should arrive soon.
Subordinate clause (mandative)	They insisted that he should resign.

Common uses of would

Use	Example
Conditional	I would go if I had time.
Polite requests	Would you help me?
Past habitual	When we were children, we would swim in the river.
Volition	He would not listen.