Category mismatches in coordination [BAK20]

Bruening, Benjamin & Eman Al Khalaf. 2020. Category mismatches in coordination revisited. Linguistic Inquiry 51(1). 1–36.

In selection-violating coordination the linearly closest conjunct to the selecting head must satisfy c-selection (§3.1): the first conjunct in VO complement position, the last conjunct when the coordination precedes its selector (subject position, OV complements, postpositions). The two rival percolation mechanisms — linear closeness (B&AK) and structural prominence (the bottom-up accounts of [Mun93], [Zha10]) — are the two modes of a single predictOrder; they agree postverbally but diverge preverbally, the configuration that empirically distinguishes them.

Only two genuine category mismatches survive in selection-violating coordination (§3.2): CP↔NP and non-ly Adverb↔Adjective, both mirroring displacement and ellipsis. We derive this enumeration structurally from a distributional map rather than stipulating it. Apparent mismatches in predication and modification (§2) are not violations but supercategory selection (Pred, Mod).

Main definitions

• FeaturePercolation — which conjunct's features reach the selecting head: linear (B&AK) vs structural (bottom-up).
• predictOrder — conjunct-order prediction from percolation mode and verb position; linearClosenessPrediction / bottomUpPrediction are its partial applications.
• coordExtension — extended distributional compatibility per Cat.
• Supercategory — the Pred / Mod supercategory features over Cat.

Main results

• percolation_diverges_preverbal — the two accounts disagree preverbally.
• subject_position_distinguishes, ov_predictions_diverge — the English-subject and OV configurations that adjudicate them.
• coordExtension_exhaustive — only CP and AdvP extend, deriving the two permitted violations rather than stipulating them.

References

[BAK20]; the cross-linguistic OV test is [Sch26].

Shared types for selection-violating coordination

inductive BrueningAlKhalaf2020.ConjunctOrder : Type

Preferred order of conjuncts in DP-CP selection-violating coordination.

• dpFirst : ConjunctOrder

  DP conjunct precedes CP conjunct.

• cpFirst : ConjunctOrder

  CP conjunct precedes DP conjunct.

@[implicit_reducible]

instance BrueningAlKhalaf2020.instDecidableEqConjunctOrder : DecidableEq ConjunctOrder

Equations

• BrueningAlKhalaf2020.instDecidableEqConjunctOrder x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance BrueningAlKhalaf2020.instReprConjunctOrder : Repr ConjunctOrder

Equations

• BrueningAlKhalaf2020.instReprConjunctOrder = { reprPrec := BrueningAlKhalaf2020.instReprConjunctOrder.repr }

def BrueningAlKhalaf2020.instReprConjunctOrder.repr : ConjunctOrder → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

Feature percolation and the directionality principle

inductive BrueningAlKhalaf2020.FeaturePercolation : Type

How selectional features percolate through &P to the selecting head.

The competing analyses of selection-violating coordination disagree on a single parameter: which conjunct's categorial features are visible to the selecting head. This parameter determines conjunct-order preferences as a function of surface position.

• structural : FeaturePercolation

  Features percolate from the structurally prominent (spec) position. The first conjunct always determines &P's categorial features, regardless of surface position relative to the verb. Analyses: [Mun93], [Zha10].

• linear : FeaturePercolation

  Features percolate from the linearly closest conjunct to the selecting head. Which conjunct is closest depends on surface position relative to the verb. Analysis: [BAK20].

@[implicit_reducible]

instance BrueningAlKhalaf2020.instDecidableEqFeaturePercolation : DecidableEq FeaturePercolation

Equations

• BrueningAlKhalaf2020.instDecidableEqFeaturePercolation x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def BrueningAlKhalaf2020.instReprFeaturePercolation.repr : FeaturePercolation → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[implicit_reducible]

instance BrueningAlKhalaf2020.instReprFeaturePercolation : Repr FeaturePercolation

Equations

• BrueningAlKhalaf2020.instReprFeaturePercolation = { reprPrec := BrueningAlKhalaf2020.instReprFeaturePercolation.repr }

def BrueningAlKhalaf2020.predictOrder (fp : FeaturePercolation) (pos : WordOrder.VerbPosition) : ConjunctOrder

Derive conjunct order preference from feature percolation mechanism.

The core principle: the conjunct whose features percolate to &P must satisfy c-selection (= must be the DP). The percolation mechanism determines which conjunct that is:

• Structural: spec (= first conjunct) → always DP-first
• Linear: closest to V → DP-first postverbally, CP-first preverbally

Equations

• BrueningAlKhalaf2020.predictOrder BrueningAlKhalaf2020.FeaturePercolation.structural pos = BrueningAlKhalaf2020.ConjunctOrder.dpFirst
• BrueningAlKhalaf2020.predictOrder BrueningAlKhalaf2020.FeaturePercolation.linear WordOrder.VerbPosition.postverbal = BrueningAlKhalaf2020.ConjunctOrder.dpFirst
• BrueningAlKhalaf2020.predictOrder BrueningAlKhalaf2020.FeaturePercolation.linear WordOrder.VerbPosition.preverbal = BrueningAlKhalaf2020.ConjunctOrder.cpFirst

theorem BrueningAlKhalaf2020.structural_position_invariant (pos₁ pos₂ : WordOrder.VerbPosition) : predictOrder FeaturePercolation.structural pos₁ = predictOrder FeaturePercolation.structural pos₂

Structural percolation is position-invariant: the structurally prominent conjunct is always first, regardless of surface order.

theorem BrueningAlKhalaf2020.linear_position_dependent : predictOrder FeaturePercolation.linear WordOrder.VerbPosition.preverbal ≠ predictOrder FeaturePercolation.linear WordOrder.VerbPosition.postverbal

Linear percolation is position-dependent: preverbal and postverbal yield different predictions.

theorem BrueningAlKhalaf2020.percolation_agrees_postverbal : predictOrder FeaturePercolation.structural WordOrder.VerbPosition.postverbal = predictOrder FeaturePercolation.linear WordOrder.VerbPosition.postverbal

The two percolation mechanisms agree in postverbal position: both predict DP-first when V precedes the coordination.

theorem BrueningAlKhalaf2020.percolation_diverges_preverbal : predictOrder FeaturePercolation.structural WordOrder.VerbPosition.preverbal ≠ predictOrder FeaturePercolation.linear WordOrder.VerbPosition.preverbal

The two percolation mechanisms diverge in preverbal position: structural predicts DP-first, linear predicts CP-first. This is the configuration that empirically distinguishes the accounts.

def BrueningAlKhalaf2020.linearClosenessPrediction : WordOrder.VerbPosition → ConjunctOrder

Linear closeness prediction (B&AK's core claim, §3.1): the linearly closest conjunct to the selecting head must satisfy c-selection.

In VO complement position: V [&P X and Y] → X is closest → DP-first. In OV complement position: [&P X and Y] V → Y is closest → CP-first (so DP is last, verb-adjacent).

This also applies to English subject position (preverbal even in VO) and postpositions (selecting head follows coordination).

Derived from predictOrder with linear percolation.

Equations

• BrueningAlKhalaf2020.linearClosenessPrediction = BrueningAlKhalaf2020.predictOrder BrueningAlKhalaf2020.FeaturePercolation.linear

def BrueningAlKhalaf2020.bottomUpPrediction : WordOrder.VerbPosition → ConjunctOrder

Bottom-up prediction (competitor account, §3.1): asymmetric &P structure makes the first conjunct structurally more prominent. The selected DP must be first, regardless of surface position relative to the verb.

Analyses: [Mun93], [Zha10].

Derived from predictOrder with structural percolation.

Equations

• BrueningAlKhalaf2020.bottomUpPrediction = BrueningAlKhalaf2020.predictOrder BrueningAlKhalaf2020.FeaturePercolation.structural

Permitted selection violations

inductive BrueningAlKhalaf2020.SelectionViolationType : Type

B&AK identify exactly two category mismatches that are permitted in selection-violating coordination (§3.2).

These parallel the categories that allow displacement and ellipsis:

1. CP↔NP: CPs can appear in NP positions (also seen in topicalization, pseudoclefts, "do so" replacement)
2. Non-ly Adv↔Adj: manner adverbs without -ly can appear in adjective positions (also seen in prenominal modification)

• cpAsNp : SelectionViolationType

  CP appearing in an NP-selecting position.

• advAsAdj : SelectionViolationType

  Non-ly adverb appearing in an adjective position.

@[implicit_reducible]

instance BrueningAlKhalaf2020.instDecidableEqSelectionViolationType : DecidableEq SelectionViolationType

Equations

• BrueningAlKhalaf2020.instDecidableEqSelectionViolationType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance BrueningAlKhalaf2020.instReprSelectionViolationType : Repr SelectionViolationType

Equations

• BrueningAlKhalaf2020.instReprSelectionViolationType = { reprPrec := BrueningAlKhalaf2020.instReprSelectionViolationType.repr }

def BrueningAlKhalaf2020.instReprSelectionViolationType.repr : SelectionViolationType → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def BrueningAlKhalaf2020.permittedViolations : List SelectionViolationType

The exhaustive list of permitted violations, justified structurally by coordExtension_exhaustive: only CP and AdvP have non-empty extensions. See violation_from_extension and extension_to_violation for the bidirectional correspondence.

Equations

• BrueningAlKhalaf2020.permittedViolations = [BrueningAlKhalaf2020.SelectionViolationType.cpAsNp, BrueningAlKhalaf2020.SelectionViolationType.advAsAdj]

theorem BrueningAlKhalaf2020.exactly_two_violations : permittedViolations.length = 2

English VO complement position

theorem BrueningAlKhalaf2020.english_is_vo : English.wordOrder.ovOrder = WordOrder.OVOrder.vo

English is VO: complements follow the selecting verb.

theorem BrueningAlKhalaf2020.english_complement_postverbal : English.wordOrder.ovOrder.verbPosition = some WordOrder.VerbPosition.postverbal

English complement position maps to postverbal.

theorem BrueningAlKhalaf2020.bak_english_complement : linearClosenessPrediction WordOrder.VerbPosition.postverbal = ConjunctOrder.dpFirst

B&AK predict DP-first in English complement position: the first conjunct is closest to V.

You can depend on [NP my assistant] and [CP that he will be on time]. ✓

[BAK20]'s (3a), from [SGWW85] (1985:165).

theorem BrueningAlKhalaf2020.accounts_agree_complement : linearClosenessPrediction WordOrder.VerbPosition.postverbal = bottomUpPrediction WordOrder.VerbPosition.postverbal

Bottom-up also predicts DP-first for English VO complements. Both accounts agree for this configuration.

English subject position: the distinguishing case

B&AK's strongest within-English evidence for closeness over first-conjunct prominence (§3.1, their (41)):

(41a) [CP That he was late all the time] and [NP his constant harassment of coworkers] resulted in his being dismissed. ✓

(41b) *[NP His constant harassment of coworkers] and [CP that he was late all the time] resulted in his being dismissed. ✗

When coordination is in subject position, it precedes the verb even in English VO. The last conjunct is closest to V. B&AK predict the NP must be last (closest), giving CP-first order. Bottom-up accounts predict DP-first regardless — wrong for this configuration.

theorem BrueningAlKhalaf2020.bak_subject_cpFirst : linearClosenessPrediction WordOrder.VerbPosition.preverbal = ConjunctOrder.cpFirst

B&AK predict CP-first in subject position: the last conjunct is closest to V, so the DP must be last.

theorem BrueningAlKhalaf2020.bottomUp_subject_dpFirst : bottomUpPrediction WordOrder.VerbPosition.preverbal = ConjunctOrder.dpFirst

Bottom-up predicts DP-first even in subject position.

theorem BrueningAlKhalaf2020.subject_position_distinguishes : linearClosenessPrediction WordOrder.VerbPosition.preverbal ≠ bottomUpPrediction WordOrder.VerbPosition.preverbal

Subject position distinguishes the two accounts within a single language (English). B&AK argue this is decisive evidence for closeness over structural prominence.

Cross-linguistic predictions

theorem BrueningAlKhalaf2020.bak_predicts_cpFirst_ov : Option.map linearClosenessPrediction WordOrder.OVOrder.ov.verbPosition = some ConjunctOrder.cpFirst

For OV languages, B&AK predict CP-first: complements precede V, so the last conjunct is closest. The DP must be last → CP-first.

theorem BrueningAlKhalaf2020.bak_predicts_dpFirst_vo : Option.map linearClosenessPrediction WordOrder.OVOrder.vo.verbPosition = some ConjunctOrder.dpFirst

For VO languages, B&AK predict DP-first.

theorem BrueningAlKhalaf2020.ov_predictions_diverge : Option.map linearClosenessPrediction WordOrder.OVOrder.ov.verbPosition ≠ Option.map bottomUpPrediction WordOrder.OVOrder.ov.verbPosition

OV is the cross-linguistic test case. Bottom-up and B&AK diverge on OV complement order.

[Sch26] tests this with German and finds DP-first (~77%), supporting bottom-up over B&AK for OV complement position.

Supercategories

inductive BrueningAlKhalaf2020.Supercategory : Type

B&AK's supercategory features unify apparent category mismatches that are not true selection violations.

Pred: NP, VP, AP, PP can all serve as predicates. A verb like become selects the supercategory Pred — specifically NP and AP, not PP (§2, their (1), (34)); selection is finer-grained than the supercategory that coordination cares about.

Mod: AP, AdvP can both modify. Prenominal position selects Mod, not specifically Adj.

• pred : Supercategory

  Predicative: NP, VP, AP, PP can all serve as predicates.

• mod : Supercategory

  Modifier: AP, AdvP can both serve as (prenominal) modifiers.

@[implicit_reducible]

instance BrueningAlKhalaf2020.instDecidableEqSupercategory : DecidableEq Supercategory

Equations

• BrueningAlKhalaf2020.instDecidableEqSupercategory x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance BrueningAlKhalaf2020.instReprSupercategory : Repr Supercategory

Equations

• BrueningAlKhalaf2020.instReprSupercategory = { reprPrec := BrueningAlKhalaf2020.instReprSupercategory.repr }

def BrueningAlKhalaf2020.instReprSupercategory.repr : Supercategory → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def BrueningAlKhalaf2020.Supercategory.cats : Supercategory → Finset Syntax.Cat

Categories belonging to each supercategory, grounded in the Cat category system from Syntax. Pred is the full predicative supercategory (B&AK's (84): Pred:{NP,AP} and friends); Mod is restricted here to the prenominal modifier categories. The inclusion order on Finset Cat gives the lattice structure.

Equations

• BrueningAlKhalaf2020.Supercategory.pred.cats = {Syntax.Cat.NP, Syntax.Cat.VP, Syntax.Cat.AdjP, Syntax.Cat.PP}
• BrueningAlKhalaf2020.Supercategory.mod.cats = {Syntax.Cat.AdjP, Syntax.Cat.AdvP}

theorem BrueningAlKhalaf2020.adjp_in_pred : Syntax.Cat.AdjP ∈ Supercategory.pred.cats

AP belongs to both supercategories.

theorem BrueningAlKhalaf2020.adjp_in_mod : Syntax.Cat.AdjP ∈ Supercategory.mod.cats

theorem BrueningAlKhalaf2020.supercats_overlap : Supercategory.pred.cats ∩ Supercategory.mod.cats = {Syntax.Cat.AdjP}

Pred and Mod overlap at exactly AP.

def BrueningAlKhalaf2020.coordExtension : Syntax.Cat → Finset Syntax.Cat

Extended distributional compatibility for coordination (§3.2). Categories that c can appear as in non-coordination contexts (displacement, ellipsis), beyond its native category.

• CP → NP: CPs can be topicalized, pseudoclefted, and pro-form replaced — NP-like distributional properties
• AdvP → AdjP: non-ly adverbs appear prenominally — AdjP-like distributional properties (only with a non-ly adverb conjoined to an AP in prenominal position, AP last; this coarse map drops those conditions)

All other categories have no extended compatibility. Combined with Supercategory.cats, this derives B&AK's "exactly two permitted violations" (§3.2).

Equations

• BrueningAlKhalaf2020.coordExtension Syntax.Cat.CP = {Syntax.Cat.NP}
• BrueningAlKhalaf2020.coordExtension (Syntax.Cat.proj UD.UPOS.ADV) = {Syntax.Cat.AdjP}
• BrueningAlKhalaf2020.coordExtension x✝ = ∅

theorem BrueningAlKhalaf2020.cp_extends_np : Syntax.Cat.NP ∈ coordExtension Syntax.Cat.CP

CP extends to NP positions.

theorem BrueningAlKhalaf2020.advp_extends_adjp : Syntax.Cat.AdjP ∈ coordExtension (Syntax.Cat.proj UD.UPOS.ADV)

AdvP extends to AdjP positions.

theorem BrueningAlKhalaf2020.coordExtension_exhaustive (c : Syntax.Cat) : coordExtension c ≠ ∅ → c = Syntax.Cat.CP ∨ c = Syntax.Cat.AdvP

Only CP and AdvP have non-empty coordination extensions. This structurally derives B&AK's "exactly two permitted violations" (§3.2) from distributional profiles rather than stipulating them as a list.

def BrueningAlKhalaf2020.SelectionViolationType.cats : SelectionViolationType → Syntax.Cat × Syntax.Cat

Map each violation type to its source and target categories. The source category can appear in a position selecting the target via coordination.

Equations

• BrueningAlKhalaf2020.SelectionViolationType.cpAsNp.cats = (Syntax.Cat.CP, Syntax.Cat.NP)
• BrueningAlKhalaf2020.SelectionViolationType.advAsAdj.cats = (Syntax.Cat.AdvP, Syntax.Cat.AdjP)

theorem BrueningAlKhalaf2020.violation_from_extension (v : SelectionViolationType) : v.cats.2 ∈ coordExtension v.cats.1

Each permitted violation corresponds to a non-empty coordExtension: the target category appears in the extension of the source.

theorem BrueningAlKhalaf2020.extension_to_violation (c : Syntax.Cat) (h : coordExtension c ≠ ∅) : ∃ (v : SelectionViolationType), v.cats.1 = c

Every non-empty coordExtension corresponds to a permitted violation. This, together with violation_from_extension, establishes a bijection between SelectionViolationType and non-empty extensions, proving the enumeration is not stipulated but derived from distributional profiles.

Structural assumptions and coordination symmetry

B&AK's derivation (§4.3) builds the syntax left-to-right rather than bottom-up, with feature checking at &P using the linearly closest conjunct. They accept asymmetric &P structure — the same assumption as the bottom-up accounts — and disagree only about the mechanism deriving predictions from it: linear closeness (B&AK) vs structural prominence (bottom-up). Both accept CoordSymmetry.asymmetric, but only the bottom-up account's predictions require it.

def BrueningAlKhalaf2020.mergeCoordSymmetry : Syntax.Coordination.CoordSymmetry

Coordination structure as adopted by both B&AK and the bottom-up accounts is asymmetric: the first conjunct (specifier) is structurally more prominent than the second (§4.3, their (82)–(83)).

Under [MCB25] nonplanar Merge, merge x y and merge y x are strictly equal (Merge is commutative on the syntactic-object carrier), so this asymmetry can no longer be grounded in Merge structure; it survives only as a stipulation on the Coord head, or as a consequence of Externalization (LCA / head directionality). The stipulation is load-bearing only for the bottom-up alternatives; B&AK's own closeness mechanism is linear-order-side and does not require it.

Equations

• BrueningAlKhalaf2020.mergeCoordSymmetry = Syntax.Coordination.CoordSymmetry.asymmetric

theorem BrueningAlKhalaf2020.closeness_is_position_dependent : linearClosenessPrediction WordOrder.VerbPosition.preverbal ≠ linearClosenessPrediction WordOrder.VerbPosition.postverbal

Despite assuming asymmetric structure, B&AK's closeness prediction is position-dependent: preverbal and postverbal yield different orders.

theorem BrueningAlKhalaf2020.bottomUp_is_position_invariant : bottomUpPrediction WordOrder.VerbPosition.preverbal = bottomUpPrediction WordOrder.VerbPosition.postverbal

Bottom-up accounts derive position-invariant predictions from the same asymmetric structure: always DP-first.

def BrueningAlKhalaf2020.FeaturePercolation.requiredSymmetry : FeaturePercolation → Option Syntax.Coordination.CoordSymmetry

Structural percolation presupposes asymmetric coordination: there must be a structurally prominent (spec) position for features to percolate from. Linear percolation requires no particular structural assumption — closeness is defined over surface strings, not tree structure.

Equations

• BrueningAlKhalaf2020.FeaturePercolation.structural.requiredSymmetry = some Syntax.Coordination.CoordSymmetry.asymmetric
• BrueningAlKhalaf2020.FeaturePercolation.linear.requiredSymmetry = none

theorem BrueningAlKhalaf2020.structural_requires_asymmetric : FeaturePercolation.structural.requiredSymmetry = some mergeCoordSymmetry ∧ FeaturePercolation.linear.requiredSymmetry = none

Both accounts adopt asymmetric structure, but only the bottom-up account's predictions require it. B&AK's closeness mechanism would make the same predictions under symmetric structure.

Postposition data

B&AK extend the closeness analysis to postpositions (§3.1, their (43)). When the selecting head is a postposition (e.g. notwithstanding), the coordination precedes it, so the last conjunct is closest and must satisfy selection (= be the NP), giving CP-first order — as in subject position and OV complements. Formally the postposition case reduces to VerbPosition.preverbal (cf. bak_subject_cpFirst).