Scope and anaphora with time arguments: The case of ‘perfect modals’

Perfect modals are modals combining with (nonfinite) perfect have—may have, must have, might have, or should have. Under their non-root construal, perfect modals yield three temporal readings of the situation-time of the propositional modal complement under their scope: (i) a present perfect construal (past situation-time relative to a present reference-time); (ii) a future perfect construal (past situation-time relative to a future reference-time); (iii) a perfect future construal (future situation-time relative to a past reference-time). The goal of this paper is to provide a unified account of the temporal readings of perfect modals within the framework developed in our previous work, where tenses and aspects are dyadic predicates of spatiotemporal ordering projecting their time arguments in the syntax as Zeit-phrases. We argue that the temporal syntax of perfect modals supports the proposal that these Zeit-Phrases can enter into anaphoric dependencies and undergo phrasal movement (QR) to higher scope positions, just as ordinary DPs/QPs can.