Modal auxiliary verbs: ability, advice, certainty, intention/willingness, obligation/absence of obligation, offers, permission, possibility, prediction, probability, requests, suggestions
Formal characteristics: defective (lack full set of forms), must be followed by a bare infinitive, act as operators
Can/could
Capacity, ability (past: could). Specific: was/were able to. Succeeded in, manage to.
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To say something is possible: ability, permission, opportunity
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May
Permission. May I leave earlier? Yes, you may leave earlier
Mustn't, can't: deny permission
Possibility, probability: less likely than can or could
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Might
Possibility, probability: less likely than may
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Shall: questions
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Determination, prediction (2nd and 3rd)
Should
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+Perf inf: sth a person didn't do, but it would have been the right thing to do
Would
2nd and 3rd conditional, I wish, if only
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Dare
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-, ?: lexical or as an operator
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Will
Volition: weak with polite requests (2ndp), intermediate with intention (1stp), strong with insistence of orders (2nd, 3rdp)
Certainty of an action, characteristic habit
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Promising, inviting offering, 1st conditional
Used to: past habit, no longer practiced