The Progressive

Mary was drawing a circle can be true when Mary drew a circle is false: she may have been interrupted. This is the imperfective paradox, and it rules out the extensional analysis of Bennett and Partee, on which a progressive is true at an interval that a longer interval of the sentence's truth in the actual world extends into the future. The imperfective of the event semantics over the actual world alone, true at an interval inside the run time of an actual event of its type, is extensional in the same way, so it makes every progressive entail its perfective. Landman takes the progressive instead to relate an actual event in progress to a possibly non-actual complete event of its type, and builds the relation from two operations. Within a world, an event grows into the events of which it is a stage until it stops. When it stops, a Stalnaker-style selection function gives the closest world where it does not, and the event is followed there if that world is a reasonable option for it, one in which it gets no further than it had a reasonable chance to get on the basis of what is internal to it. The worlds and events reached form its continuation branch, and e is in progress toward P holds when some event on the branch is of type P.

So whatever gets completed was in progress during its development, even against all odds. For a process interrupted n times, the progressive holds exactly when each of the n counterfactual continuations is reasonable. Mary was crossing the street when one truck hit her, and when the second truck behind it would have, but she was not wiping out the Roman army when the first soldier killed her; by contrast, the inertia worlds of Dowty's progressive, where everything takes its normal course, contain the truck, so it makes Mary's crossing false. These scenarios decide the paper's judgments, where the imperfective of the event semantics gets the interrupted drawing wrong.

Implementation notes

• Events are ordered by stage-of, e ≤ f when e is a stage of f. Part-of, which the paper uses only to motivate stages, is not modelled.
• An event occurs in some worlds and not in others, and has the same run time, the temporal trace of the event semantics, in each world where it occurs. The paper's trace is relative to a world, but none of its definitions compares the intervals of an event across worlds.
• An event stops when it goes on but nothing of which it is a stage goes on at a later-ending interval; the paper's restriction to non-final intervals is dropped, since the branch only jumps to a world where the event continues, and the paper presupposes that the closest such world exists.
• The branch jumps from a maximal event of the world, which then stops (stops_of_maximal); it is the maximal element of the continuation stretch, since every event of which a branch event is a stage is on the branch. The paper's constraints on stage-of within a world (§2.2) and its Activity Postulate are not imposed; the activity half of the paradox is activity_of_prog, under the hypothesis the postulate supplies, that a process stage of an event of an activity type is of that type.
• In the interrupted processes, the events are intervals, the event domain of the event semantics with the identity trace, so Aspect.IMPF and Aspect.PRFV apply to the same models. World k removes the first k interruptions, and the closest world is the first one from the current world on. Tense is not modelled: a progressive is evaluated at its first stage.
• The swimmer of (17) and the soldier of (20) need five continuations and have a reasonable reach of two; only whether the reach covers the interruptions matters (prog_interrupted_iff).
• Dowty's progressive is Dowty1979.prog, his (25), applied to the run times of the events of a type. Landman's statement of it (p. 3) takes the longer interval after the inertia world; the two agree when, as for the truck, the actual world is the only inertia world.

Errata

• The definition of stopping (p. 24) says that f, going on at j, stops when nothing of which it is a stage goes on beyond i, the interval of e. Since f is a stage of itself, f would then never stop at an interval ending later than i, and the continuation branch could not leave the world of e; j is meant, and Stops reads it.

TODO

• The rival proposals of §1, the normality, subjunctive and part-of proposals, are not formalized, nor the stage kinds of the Activity Postulate (process, planning and pause), the intensionality of the object position in (9) and (10), or the perspectives of the appendix.

References

• Landman 1992, The Progressive
• Bennett & Partee 1972, Toward the Logic of Tense and Aspect in English
• Dowty 1979, Word Meaning and Montague Grammar: The Semantics of Verbs and Times in Generative Semantics and in Montague’s PTQ formalized
• Stalnaker 1968, A Theory of Conditionals formalized