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What are semi-modal verbs?
From Politely Getting Things Done, Chapter Seven:Modals also have phrasal or periphrastic counterparts which act more like regular verbs with verb agreement, tense and the addition of to before the verb. Sometimes these are called semi-modals. They are fairly recent grammatical developments. They appear mostly in speech, where most grammatical changes first appear, rather than in writing, which tends to be more conservative.There's another list here Grammar and Mechanics (page 2).can, could >>> be able towill, shall >>> be going to (gonna), be about tomust >>> have to (hafta), have got toshould >>> be to, be supposed tomay, might >>> be allowed to, be permitted to
Click here also Modals in English Language Teaching and scroll down to What are modal verbs? It explains how linguists deal with semi-modals.
And there's also this one:Uses of Modals and Semi-modals