The Semantic Ingredients of Imperfectivity in Progressives, Habituals, and Counterfactuals

Many languages express progressive and habitual readings with one imperfective form, as the Italian Gianni fumava 'Gianni was smoking / used to smoke'. Ferreira derives both readings from one operator built from three ingredients. The temporal ingredient is ongoingness: the reference interval lies within the run time of an event. The modal ingredient is Portner's: the event exists in every best world of a circumstantial modal base for the event description at the reference interval, ranked by an ordering source of propositions that the eventuality is not interrupted. The mereological ingredient is a number parameter: the singular operator keeps the minimal events of the description, and the plural operator its sums of non-overlapping events, so that the progressive is about a single ongoing event and the habitual about an ongoing plurality. The operator is the modal imperfective of the event semantics, Aspect.IMPF, over Portner's best worlds, applied to the description refined for number.

So John was crossing the street is true when a bus stops him, but John was crossing the Atlantic is false of an ordinary swimmer, and John plays soccer is true of a regular player until an accident leaves him unable to move his legs; these scenarios decide the paper's judgments. A singular event of a description is never a plural one (sg_disjoint_pl). Statives have no minimal elements, so their imperfectives cannot be progressive, which is why imperfective statives pattern with habituals. Over a modal base that admits only the actual world, the operator is Kratzer's extensional imperfective, the reference interval within the run time of an actual event.

Implementation notes

• The number parameter is an operator on predicates of events: the singular is Mereology.atomize, the minimal elements, and the plural is PL, (12).
• The modal base and ordering source are Modality.Backgrounds projected from the description and the reference interval, as in (53), and the progressive's event-relative form is Aspect.InProgress.
• Ongoingness is inclusion, i ⊆ τ(e), the relation of Aspect.IMPF; over the world of evaluation alone it is Kratzer's extensional Aspect.UNBOUNDED (Aspect.impf_singleton).
• The run time of a sum is the convex hull of the run times of its parts, so Ferreira's inclusion of an interval in a plural interval (31) is inclusion in the hull, and (33) holds. The habitual scenario takes its events to be sets of games ordered by inclusion.

Errata

• (111) applies MOD to its arguments in the order MOD(w)(i)(…), though it defines MOD as λ℘.λi.λw; read in its defined order it computes BEST from the composite predicate, where (52) and (58) compute it from the description ℘, which IMP follows.

TODO

• The boundedness presuppositions (105) and (109), adverbs of quantification (§2.4), the temporal convexity of statives (96)–(98), and counterfactuals (§3) are not formalized.

References

• Ferreira 2016, The Semantic Ingredients of Imperfectivity in Progressives, Habituals, and Counterfactuals
• Portner 1998, The Progressive in Modal Semantics formalized
• Kratzer 1998, More Structural Analogies between Pronouns and Tenses formalized
• Kratzer 1991, Modality