(2000) proposed a formal treatment of Minami's hierarchy under the framework of HPSG and Discourse Representation Theory.
their analysis focused only on the interpretation of temporal relation between the events described in subordinate and matrix clauses, and it simply reformulates Minami's hierarchy as 'hierarchy feature' which can take value A, B, C, and D. Minami's (and Yoshimoto's) work seems to capture a surface ranking for such combination with using somewhat tentative levels, and there is no answer to the question: Which linguistic information is the origin of HCF (and his level of hierarchy)?