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modal auxiliary
noun
an auxiliary verb (such as `can' or `will') that is used to express modality
Syn: ↑modal auxiliary verb, ↑modal verb, ↑modal
Hypernyms: ↑auxiliary verb

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noun
: a verb or a grammatical form resembling a verb that is characteristically used with a verb of predication and expresses a modal modification (as can, shall, will, must, might, ought, could, should, would, may, need, dare) and that in English differs formally from other verbs in lacking -s, -ing, and past-tense forms and shares with other auxiliaries the affixing of negative -n't

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Gram. any of the group of English auxiliary verbs, including can, could, may, might, shall, should, will, would, and must, that are used with the base form of another verb to express distinctions of mood.
[1930-35]

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modal auxiliary or modal verb noun
In English, any of the verbs can, could, may, might, will, would, shall, should, must and ought, and sometimes need, dare and used to, which modify the sense of a main verb and express concepts such as politeness, certainty and obligation
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Main Entry:mode

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modal auxiliary UK US noun [countable] [singular modal auxiliary plural modal auxiliaries] linguistics
a modal verb
Thesaurus: verb forms and tenseshyponym

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modal auxiliary,
one of a set of auxiliary verbs in English, including words like may, can, must, would, and should, that indicates the mood of the verb with which it is used.

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modal [ˈməʊdl] [ˈmoʊdl] (also modal ˈverb, modal auˈxiliary, modal auˈxiliary verb) noun (grammar)
a verb such as can, may or will that is used with another verb (not a modal) to express possibility, permission, intention, etc.
compare auxiliary
Derived Word:modal
See also:modal auxiliary verb modal verb  
Word Origin:
[modal] mid 16th cent.: from medieval Latin modalis, from Latin modus ‘measure’, from an Indo-European root shared by mete; compare with mood in its grammatical sense.  
Grammar Point:
modal verbs
The modal verbs are can, could, may, might, must, ought to, shall, should, will and would. Dare, need, have to and used to also share some of the features of modal verbs.
Modal verbs have only one form. They have no -ing or -ed forms and do not add -s to the 3rd person singular form:

He can speak three languages.

She will try and visit tomorrow.

Modal verbs are followed by the infinitive of another verb without to. The exceptions are ought to and used to:

You must find a job.

You ought to stop smoking.

I used to smoke but I gave up two years ago.

Questions are formed without do/does in the present, or did in the past:

Can I invite Mary?

Should I have invited Mary?

Negative sentences are formed with not or the short form -n’t and do not use do/does or did.
You will find more help with how to use modal verbs at the dictionary entries for each verb.

Useful english dictionary. 2012.