A re-analysis and classification of English modals are proposed. Most of the candidates for inclusion in the modal category are eliminated since they are independently generated as verbs, adjectives, and adverbs. Those included are further classified into the 'pure' (M) and the 'quasi' (Q) by their ability to combine internally in the auxiliary. On syntactic grounds, then, Chomsky's re-writing rule is revised as. Aux -> Tense(M)(Q)^n(have + en)(Q)^n(be + ing) (Q)^n. Based on this segmentation, both modals and quasi-modals are examined regarding their selectional characteristics as well as their relationships to certain transformation. The paper concludes that despite tenuous evidence surrounding their semantics, the syntax of English modal constructions can be described by a single rule.
Hakutani, Yoshinobu (1972). The Syntax of Modal Constructions in English. Elsevier 30 301-332. doi: 10.1016/0024-3841(72)90059-9. Retrieved from https://oaks.kent.edu/engpubs/164