Liu & Yip 2026: Again, finiteness, and split aspect in Chinese languages #
@cite{liu-yip-2026} (NLLT 44:25, doi 10.1007/s11049-026-09708-5).
Paper's central claims #
(1) Hierarchical, size-based finiteness in Chinese. Three clause sizes: Type I (CP, finite), Type II (TP, nonfinite without Aspect Restructuring), Type III (vP, nonfinite with Aspect Restructuring). (2) Split aspect. Two aspectual projections in the spine: AspP_outer above vP, AspP_inner inside vP. (3) Asymmetry of again-elements. Mandarin preverbal you and Cantonese postverbal -faan associate with AspP_outer (and may exhibit "exceptional scopal behavior" — you-skipping by movement+reconstruction; -faan-lowering by Agree). Mandarin zai and Cantonese -gwo associate with AspP_inner (and never scope-mismatch). (4) Defective intervention. When the embedded clause is TP-sized, its embedded AspP_outer blocks the matrix probe's reach to the embedded again-element. (5) @cite{wurmbrand-lohninger-2023} ICH (proposition > situation > event) instantiated by Chinese as CP > TP > vP. (6) vP is the minimal nonfinite size. Empirical: AspP_inner is mandatory above V; aspect-lowering and -gwo-lowering systematically don't occur.
What this Studies file commits to substrate #
No new substrate files. The @cite{wurmbrand-lohninger-2023} ICH, the @cite{wurmbrand-2001} truncation operator, and the @cite{pesetsky-2021} Exfoliation primitive all violate the ≥ 2-paper-anchor graduation rule. They live as local definitions here, ready to graduate when a second study consumes them.
The substrate-level addition @cite{liu-yip-2026}'s analysis does motivate is the bipartite split-aspect typing:
AspFlavorandAspHead, landed inTheories/Syntax/Minimalist/Aspect.leanparallel toVoiceHead { flavor }. That commitment is independent of the analytical claims of this paper — it is consumed by @cite{travis-2010}, @cite{macdonald-2008}, @cite{tsai-2008}, @cite{sybesma-2017}, and @cite{liu-yip-2026} jointly — so it warranted substrate placement.
What this Studies file does NOT commit to #
Defective intervention is NOT bilateral labeling. @cite{liu-yip-2026}'s intervener is a featurally-matching head occupying a probe position (@cite{chomsky-2000} defective intervention), not a category in a bilateral label (@cite{keine-2020} horizon opacity). The two coincide on the Type II / Type III contrast but make distinct predictions on featural mismatch. The
defectiveInterventionpredicate below uses head-as-intervener; it does not callProbeProfile.transparentToLabel.Aspect-lowering and -faan-lowering are parallel, not the same. Both involve matrix-AspP_outer Agree across a vP boundary, but the empirical diagnostics differ (e.g., -zhe_CONT vs -zhe_IPFV asymmetry; -gwo not lowering in Cantonese). No reduction theorem is asserted.
The @cite{wurmbrand-lohninger-2023} ICH is not a baked-in
LinearOrderwith an implication on transparency. The order onComplementClassis independent of the claim that transparency is downward-closed; the latter is a theorem about a transparency relation, not a definitional property.Minimal-vP is empirical, not structural. Encoded as a per-fragment drift sentry, falsifiable by a single new datum.
Cross-framework reconciliation #
§11 below documents divergences with HPSG (lexical-rule analysis of
"you-skipping"), Dependency Grammar (no AspP, no ICH), CCG (forward
composition), Fragments/Italian/Modals.lean's @cite{hacquard-2006}
restructuring substrate, Phenomena/Control/Studies/Landau2015.lean's
ControlTier, and Theories/Syntax/Minimalist/Phase.lean. The
@cite{cinque-2006} vs. @cite{wurmbrand-2001} restructuring rivalry is made
explicit in §10 as a refutation theorem candidate.
@cite{liu-yip-2026}'s Type I: finite (CP). Selected by xiangxin 'believe', shuo 'say' etc.; blocks you-skipping and -faan-lowering.
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@cite{liu-yip-2026}'s Type II: nonfinite without Aspect Restructuring (TP). Selected when the predicate licenses TP but blocks -faan-lowering via embedded AspP_outer intervention.
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@cite{liu-yip-2026}'s Type III: nonfinite with Aspect Restructuring (vP). Selected by xiang 'want', rang 'let' etc.; permits you-skipping and -faan-lowering.
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The Implicational Complementation Hierarchy of @cite{wurmbrand-lohninger-2023}: proposition > situation > event in transparency-decreasing order.
Local to this Studies file; promotion to Theories/Syntax/Complementation/
is contingent on a second paper-anchored consumer (see Phenomena/Control
studies and Phenomena/Complementation/Studies/Grano2024.lean as candidate
second sites).
LinearOrder is not derived: the implicational content of the ICH is
a theorem about a transparency relation, not a structural property of
the class lattice. The order here is just the enum's natural one
(event < situation < proposition); the implicational claim is
transparency_downward_closed below.
- event : ComplementClass
Smallest, most transparent: vP-level event reports.
- situation : ComplementClass
Mid: TP-level situation reports.
- proposition : ComplementClass
Largest, most opaque: CP-level proposition reports.
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Equations
- Phenomena.Complementation.Studies.LiuYip2026.instDecidableEqComplementClass x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- One or more equations did not get rendered due to their size.
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Numeric rank for ComplementClass: event = 0, situation = 1, proposition = 2.
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Project a ComplementSize onto the @cite{wurmbrand-lohninger-2023}
3-tier ComplementClass, by fValue thresholds. This is
@cite{liu-yip-2026}'s Chinese-specific mapping (the paper notes
explicitly that other languages may calibrate differently). The Studies
file instantiates the mapping; a richer cross-linguistic substrate would
parameterize it per-language.
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- One or more equations did not get rendered due to their size.
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@cite{wurmbrand-2001}-style restructuring: drop the topmost projected
head from a ClauseSpine. Returns none if the spine has only one
head (the floor).
Local to this Studies file. Fails the ≥2-consumer rule for substrate;
promotion candidate when Fragments/Italian/Modals.lean's informal
restructuring discussion gets a Studies file or when a
@cite{wurmbrand-2014} study lands.
Implementation: the dropLast of an at-least-2-element list is non-empty,
proved via the [x, y :: rest] pattern's structural guarantee.
Equations
- Phenomena.Complementation.Studies.LiuYip2026.restructure { projectedHeads := [], nonempty := h } = absurd Phenomena.Complementation.Studies.LiuYip2026.restructure._proof_1 h
- Phenomena.Complementation.Studies.LiuYip2026.restructure { projectedHeads := [head], nonempty := nonempty } = none
- Phenomena.Complementation.Studies.LiuYip2026.restructure { projectedHeads := x_1 :: y :: rest, nonempty := nonempty } = some { projectedHeads := x_1 :: (y :: rest).dropLast, nonempty := ⋯ }
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Restructuring strictly decreases spine length (when defined).
The proof unfolds via the structural constructors of ClauseSpine.
@cite{liu-yip-2026}'s defective intervention (@cite{chomsky-2000}): an embedded head of the same category as the matrix probe blocks Agree, regardless of bilateral labeling. The featural-compatibility check enforces that intervention is by an element occupying an embedded probe position, not by a category in a sister's label.
intervenes returns true when the embedded head's selectional
requirement (e.g. Asp_outer's [+D] dynamicity expectation) overlaps with
the matrix probe's expectation in a way that creates a defective
intervention configuration. The simplest such check: same-flavor +
same-or-compatible selectional spec.
This predicate deliberately does NOT call
ProbeProfile.transparentToLabel — head-as-intervener and label-as-locus
diverge on featurally-mismatched probes.
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- One or more equations did not get rendered due to their size.
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Studies-side projection: Mandarin you 'again' is typed as an
AspP_outer-associated probe-bearing head with a [+D] dynamicity
selectional restriction (per @cite{lin-liu-2009}, building on
@cite{shen-2004}). The lexical entry in Fragments/Mandarin/Particles.lean
carries only the presupposition trigger; the syntactic typing here
is @cite{liu-yip-2026}'s analytical commitment.
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Studies-side projection: Mandarin zai 'again' is typed as an AspP_inner-associated bare head, no dynamicity restriction.
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Studies-side projection: Cantonese -faan 'again' is AspP_outer-associated but, unlike Mandarin you, does NOT carry a [+D] selectional restriction (it is compatible with stative jau 'have' per @cite{liu-yip-2026}).
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Studies-side projection: Cantonese -gwo (repetitive use) is AspP_inner-associated. Its experiential use is also AspP_inner per the lexical entry, but pragmatically distinct.
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Mandarin you and Cantonese -faan are BOTH outer-aspect, but only
you carries [+D]. Encoding -faan with
selectsDynamicity = some .dynamic would over-predict (it would force
incompatibility with stative jau).
Generalization I (@cite{liu-yip-2026}): in Mandarin, an again-element exhibits exceptional scopal behavior IFF it is outer-aspect-associated.
On the substrate: youAspHead.isOuter = true (you may skip);
zaiAspHead.isOuter = false (zai may not). The empirical content is the
biconditional between AspFlavor and the scope-mismatch facts the paper
documents.
Generalization I (Cantonese counterpart): -faan (outer) may lower; -gwo (inner) may not.
Generalization II (@cite{liu-yip-2026}): the exceptional scopal behavior of again may cross nonfinite (vP) but not finite (CP) clause boundaries.
On the substrate: this is an instance of upward entailment of opacity
(Probe.lean upward_entailment_label). Stated here without invoking
bilateral labeling — see §5 above. The content is that for any matrix
again-bearing AspO probe, the complement clause's size determines
transparency: vP transparent, TP / CP opaque.
Correlation I (@cite{liu-yip-2026}, Mandarin): an again-element exhibits exceptional scopal behavior IFF it cannot surface in an embedded nonfinite clause without a dynamic ([+D]) aspect.
On the substrate: this is the consequence of Mandarin you's
selectsDynamicity = some .dynamic. zai, with no such restriction,
can attach to either dynamic or stative complements but never scopes
mismatch.
Correlation II (@cite{liu-yip-2026}): an again-element exhibits exceptional scopal behavior IFF it is structurally higher than aspectual elements.
On the substrate: AspO has higher defaultFLevel (2) than AspI (1).
Outer you / -faan are above the inner aspectual elements;
inner zai / -gwo are not.
The minimal-vP claim is an empirical generalization about Chinese, not a structural property derived from substrate. Stated here as a per-fragment assertion that every nonfinite-clause-taking predicate in the Mandarin and Cantonese fragments selects a complement of size ≥ vP. Falsifiable by a single new datum.
All Mandarin nonfinite-takers (xiang, rang, quan, bi, dasuan, shefa)
have complementType = .infinitival, consistent with vP-as-floor and
falsifiable by a single new datum. The Fragment-side companion is
Fragments.Mandarin.Predicates.liuyip_partition.
All Cantonese nonfinite-takers select [.vP] per the per-language
fragment classification (@cite{liu-yip-2026}).
Internal tension in the @cite{liu-yip-2026} architecture #
There is a hidden incoherence: the spine substrate (ClauseSpine +
AspFlavor.outer / inner always projected when present) commits to
@cite{cinque-2006}'s "always project all functional heads" view; the
restructuring operator above (truncate the topmost head) commits to
@cite{wurmbrand-2001}'s "remove projection on restructuring" view. These
are direct rivals on the same Chinese aspect data.
The current formalization adopts both — and lives with the tension — because:
(a) The split-aspect substrate (AspHead { flavor }) is theory-neutral:
a flavor field on a single Cat.Asp constructor doesn't itself say
that AspP_outer is always projected. Languages can opt in to
projecting only one flavor.
(b) The local restructure operator above is Wurmbrand-flavored, not a
cross-framework commitment. A Cinque-flavored alternative would
leave the spine unchanged but mark some heads as silent —
trivially, id. The substrate accommodates both projections; the
rivalry is visible rather than hidden.
The sharp refutation theorem
¬ (Wurmbrand.truncated.projects .Asp ↔ Cinque.full.projects .Asp) is
contingent on a Cinque-style "always project" formalization landing in
Theories/Syntax/Minimalist/. Until then, the rivalry is documented in
prose, not theorem.
A trivial Cinque-flavored "restructuring" (identity) for comparison
with the Wurmbrand-flavored restructure above. @cite{cinque-2006}'s
claim is that restructuring is projection-marking, not truncation;
structurally, the spine is unchanged.
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Sister-framework treatments of "you-skipping" / -faan-lowering #
Each major sister framework analyzes the same data via a fundamentally different mechanism. This section documents the divergences without attempting bridge theorems (which would require the sister frameworks to have Studies-level Chinese formalizations they currently lack):
HPSG (
Theories/Syntax/HPSG/Core/Basic.lean): no clausal spine, no AspP, no ICH. The "you-skipping" pattern would naturally be a lexical rule on argument structure (compareLexicalRules.lean:36-95'spassiveRule,dativeShiftRule,resultativeRule). @cite{liu-yip-2026}'s movement+reconstruction has no HPSG analog. SILENT DIVERGENCE.Dependency Grammar (
Phenomena/Complementation/Studies/Osborne2019Control.lean): control and raising are structurally identical in DG; AspP is absent. "you-skipping," restructuring, and -faan-lowering would all bexcompplus enhanced-edge propagation. SILENT DIVERGENCE (irreconcilable at substrate level; bridgeable only at the empirical prediction level).CCG (
Theories/Syntax/CCG/Core/Basic.lean,Scope.lean): scope mismatch is type-shifting + composition. you's skipping naturally maps to forward composition; no movement+reconstruction needed. A bridge theoremLiuYip.youSkipping iff CCG.derivableViaCompositionis tractable on a small fragment but not attempted here.Fragments/Italian/Modals.leanhas a developed restructuring substrate based on @cite{rizzi-1978} + @cite{hacquard-2006} (event-relativity analysis). The @cite{liu-yip-2026} formalization here uses a @cite{wurmbrand-2001} truncation operator (§4 above). The two are direct rivals; integration with the Italian substrate would be a productive next step but is deferred (the Italian file currently has no Wurmbrand-truncation bridge of its own).Phenomena/Control/Studies/Landau2015.leanhasControlTier(predicative vs logophoric) cross-classifying CTPs along an axis the @cite{wurmbrand-lohninger-2023} ICHComplementClass(event/situation/proposition) parallels. A bridge theoremLiuYip.proposition → Landau.logophoricis candidate future work; both Studies files currently formalize their own complement-class projections without sharing substrate.Theories/Syntax/Minimalist/Phase.leanhas @cite{chomsky-2000} / @cite{chomsky-2001} phase machinery (PICStrength). @cite{liu-yip-2026}'s intervention is by AspP_outer, a non-phase head — defective intervention is a third locality regime alongsidePICStrength.{strong, weak, linearizationBound}. The current formalization silently bypasses thePhasesubstrate. Resolution: either extendPICStrengthwith a "head-as-intervener" case, or add explicit prose noting the alternative locality model.
The local ComplementClass projects to the existing theory-neutral
surface enum Typology.Complementation.ComplementClauseStructure.
This converts the planned ICH from a parallel third axis into a
projection over substrate that already serves @cite{deal-2026},
@cite{landau-2015}, @cite{cristofaro-2013}, and @cite{noonan-2007}
— the interconnection-density discipline CLAUDE.md describes.
Note: the projection collapses @cite{wurmbrand-lohninger-2023}'s
three classes onto two surface patterns (barePropositionalCP for
proposition, abarInternalCP for situation/event). The collapse is
correct for Chinese but may not generalize.
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Deferred items #
@cite{pesetsky-2021} Exfoliation: not formalized here. The
shuo-CP puzzle @cite{liu-yip-2026} resolve via Exfoliation (CP layer peelable under A-dependency) is left as prose. Promotion to a substrate operator awaits a second consumer.Theories/Semantics/Again/substrate: a uniform again-presupposition substrate (@cite{von-stechow-1996} / @cite{beck-2006} parameterization) is recommended but not landed. Without it, every again-element's presupposition is encoded independently in its Fragment lexical entry, which silently commits to an anti-decompositional account when it type-equates you's repetitive reading with zai's. The substrate module is deferred until a German-wieder or English-again study joins.The repetitive-vs-restitutive distinction: explicitly bracketed by @cite{liu-yip-2026} as out of scope. The Mandarin
youFragment entry currently encodes only the repetitive reading; ayou_restitutivecompanion entry would be a small addition if needed.The minimal-vP empirical claim (§9): per-fragment drift sentries here cover Mandarin (6 verbs) and Cantonese (5 verbs). A larger cohort, especially for typologically distant languages claimed to have similar restructuring, would strengthen the empirical content.
@cite{wurmbrand-2014} restructuring data (German / Romance): the local
restructureoperator is @cite{wurmbrand-2001}-flavored and tested only on Chinese. @cite{wurmbrand-2014}'s lexical / functional restructuring dichotomy is a richer typology this Studies file does not yet engage.