Rouillard 2026: Temporal in-Adverbials and the Maximal Informativity Principle #

@cite{rouillard-2026} @cite{fox-hackl-2006} @cite{fox-2007} @cite{beck-rullmann-1999} @cite{krifka-1989} @cite{krifka-1998} @cite{vendler-1957} @cite{ladusaw-1979} @cite{iatridou-zeijlstra-2021} @cite{hoeksema-2006} @cite{gajewski-2011} @cite{von-fintel-iatridou-2019}

@cite{rouillard-2026} "Maximal informativity accounts for the distribution of temporal in-adverbials" (Linguistics and Philosophy 49:1–56).

Core contribution #

Temporal in-adverbials (TIAs) lead a double life:

E-TIAs ("wrote a paper in three days") measure event durations. Acceptable only with telic VPs.
G-TIAs ("hasn't been sick in three days") measure gap durations. NPI behavior: acceptable only in negative perfects.

Both distributional restrictions follow from a single principle: the Maximal Informativity Principle (MIP). For some constituent γ containing the TIA, the numeral must be capable of being the maximally informative value of γ's derived property. Where no maximally informative numeral exists ("information collapse"), the TIA is blocked.

Architecture of the formalization #

This file consolidates Rouillard's formal apparatus and the empirical verification into a single Studies file. The companion MaximalInformativity.lean was deleted in this rebuild — its content was absorbed here, with substrate primitives lifted to Core.Scale and Core.Time.Interval.Generalized.

Sections:

Re-export of substrate (Core.Scale informativity primitives).
TimeMeasure typeclass (replaces the prior MeasureFun struct).
Prior time spans over GInterval (open/closed boundary tags structurally carried, eliminating the prior PERF_open hand-waving).
E-TIA semantics: eTIAProperty.
G-TIA semantics over open generalized intervals: gTIAPropertyOpen.
The MIP licensing predicate (imported from Entailment.Extremum), combining AdmitsOptimum (atelic-collapse failure mode) with per-world IsLeast / IsGreatest from mathlib (no-extremum failure mode).
E-TIA: HasSubintervalProp → IsConstant → ¬ AdmitsOptimum (atelic block).
E-TIA: telicity → upward monotone → IsLeast {y | P y w} exists at event-duration.
G-TIA: geometric no-smallest-open-PTS (the density witness Rouillard uses). The full MIP-collapse claim under just [DenselyOrdered Time] with ℕ-valued measure does NOT follow without additional threshold-richness assumptions on the world space; we prove the geometric witness and note the gap. (See § 9 docstring for details.)
G-TIA negative: downward monotone → IsGreatest {y | P y w} exists at gap-length.
Boundedness pipeline (Vendler→Telicity→MereoTag→Boundedness, used by LicensingPipeline for the empirical predictions in § 13).
Paper-specific apparatus (TIAType, AdverbialPosition, projection from consensus Fragment fields).
E-TIA empirical data (Prop fields, decided via the boundedness chain).
G-TIA empirical data (Prop fields, decided via polarity ∧ perfect).
Table 1 (8 cells of paper eq. (112), survivor derived not stipulated).
Stacking constraint (paper §3.2, ex. 60).
Since-when questions (paper §5.2).
Fragment bridges (consensus → Rouillard projection).

Scope notes #

Cross-framework refutation theorems (Ladusaw 1979 DE-overprediction, Krifka 1989 ATM-vs-QUA divergence, Champollion stratified reference divergence, Pancheva/Kiparsky perfect bridge) are out of scope for this file by user direction; they belong in dedicated cross-framework Studies.
The LicensingMechanism enum + mip_subsumes_de strawman of the prior file is dropped — a real DE comparison would need to engage Phenomena/Polarity/Studies/Ladusaw1979.lean rather than stipulate.
The "Kennedy–Rouillard isomorphism" framing of the prior file's § 7 is dropped — Rouillard does not invoke Kennedy adjectival scales. The boundedness chain is retained as substrate-internal plumbing.