Anomalous Finites: Venn Diagram 11 Modals 2
Most probably, the best explanation comes from Encarta:
'modal auxiliary
(plural mo·dal aux·il·ia·ries)
noun
kind of verb: a verb used with other verbs to
express such ideas as permission, possibility, and necessity.
The modal auxiliaries in English grammar are "can," "could," "may," "might," "must," "ought to," "shall," "should," "will," and "would." Some classifications also include "dare," "need," and "used."
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