@cite{bill-etal-2025} — DP Conjunction Complexity

"Is DP conjunction always complex? The view from child Georgian and Hungarian" Semantics & Pragmatics 18, Article 5, 1-20.

Main Question

@cite{mitrovic-sauerland-2014} claim DP conjunction universally decomposes into J (set intersection) + MU (subset) + ☉ (type-shifter). Combined with the Transparency Principle — children prefer 1-to-1 form-meaning mappings — this predicts J-MU expressions (where all pieces are overt) should be easier for children to comprehend than J-only or MU-only.

Experiment

Act-out task: children and adults hear conjunctive sentences and manipulate objects to match. Two DVs: accuracy and sentence-played-n (replay count).

Key Findings

• Georgian children: J-MU sentences required significantly more replays than J or MU sentences (opposite of prediction). No difference between J and MU.
• Hungarian: no significant sentence-type effects detected on either measure. (Null result — could reflect ceiling effects or insufficient power.)
• Adults: near-ceiling in both languages.

Theoretical Significance

Results challenge both Mitrović & Sauerland's universal decomposition and alternative accounts.

Semantic Connection

The M&S decomposition maps directly onto Montague/Conjunction.lean:

• J = genConj (Partee & Rooth's generalized conjunction / set intersection)
• MU = inclFunc (INCL schema / subset relation)
• ☉ = typeRaise (individual → singleton set / generalized quantifier)

inductive Phenomena.Coordination.Studies.BillEtAl2025.ConjunctionStrategy : Type

Cross-linguistic conjunction strategy.

@cite{mitrovic-sauerland-2014} decompose DP conjunction into three semantic pieces: J (set intersection), MU (subset), ☉ (type-shifter). Languages vary in which pieces are overtly realized.

• jOnly : ConjunctionStrategy

  Only J particle overt (e.g., English "and", Hungarian "és", Georgian "da")

• muOnly : ConjunctionStrategy

  Only MU particles overt (e.g., Japanese "mo...mo", Hungarian "is...is", Georgian "-c...-c")

• jMu : ConjunctionStrategy

  Both J and MU overt (e.g., Hungarian "is és...is", Georgian "-c da...-c")

instance Phenomena.Coordination.Studies.BillEtAl2025.instDecidableEqConjunctionStrategy : DecidableEq ConjunctionStrategy

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.instDecidableEqConjunctionStrategy x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Coordination.Studies.BillEtAl2025.instBEqConjunctionStrategy.beq : ConjunctionStrategy → ConjunctionStrategy → Bool

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.instBEqConjunctionStrategy.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Coordination.Studies.BillEtAl2025.instBEqConjunctionStrategy : BEq ConjunctionStrategy

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.instBEqConjunctionStrategy = { beq := Phenomena.Coordination.Studies.BillEtAl2025.instBEqConjunctionStrategy.beq }

def Phenomena.Coordination.Studies.BillEtAl2025.instReprConjunctionStrategy.repr : ConjunctionStrategy → ℕ → Std.Format

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instance Phenomena.Coordination.Studies.BillEtAl2025.instReprConjunctionStrategy : Repr ConjunctionStrategy

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.instReprConjunctionStrategy = { reprPrec := Phenomena.Coordination.Studies.BillEtAl2025.instReprConjunctionStrategy.repr }

def Phenomena.Coordination.Studies.BillEtAl2025.ConjunctionStrategy.overtMorphemeCount : ConjunctionStrategy → ℕ

Number of overt functional morphemes per strategy.

Under @cite{mitrovic-sauerland-2016}, the underlying structure always has 3 semantic pieces (J + MU₁ + MU₂). What varies is how many are pronounced.

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.ConjunctionStrategy.jOnly.overtMorphemeCount = 1
• Phenomena.Coordination.Studies.BillEtAl2025.ConjunctionStrategy.muOnly.overtMorphemeCount = 2
• Phenomena.Coordination.Studies.BillEtAl2025.ConjunctionStrategy.jMu.overtMorphemeCount = 3

def Phenomena.Coordination.Studies.BillEtAl2025.ConjunctionStrategy.semanticPieceCount : ℕ

Under @cite{mitrovic-sauerland-2016}, there are always 3 semantic pieces. The transparency ratio measures how many are overtly realized.

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.ConjunctionStrategy.semanticPieceCount = 3

def Phenomena.Coordination.Studies.BillEtAl2025.ConjunctionStrategy.predictedTransparency : ConjunctionStrategy → ℕ

@cite{mitrovic-sauerland-2016} + Transparency Principle predicts: more overt morphemes → easier to acquire (closer to 1-to-1 form-meaning mapping).

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.ConjunctionStrategy.predictedTransparency = Phenomena.Coordination.Studies.BillEtAl2025.ConjunctionStrategy.overtMorphemeCount

structure Phenomena.Coordination.Studies.BillEtAl2025.ConjParticle : Type

A conjunction particle in a specific language.

• language : String
• form : String
• gloss : String
• role : String
• boundMorpheme : Bool

instance Phenomena.Coordination.Studies.BillEtAl2025.instReprConjParticle : Repr ConjParticle

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.instReprConjParticle = { reprPrec := Phenomena.Coordination.Studies.BillEtAl2025.instReprConjParticle.repr }

def Phenomena.Coordination.Studies.BillEtAl2025.instReprConjParticle.repr : ConjParticle → ℕ → Std.Format

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def Phenomena.Coordination.Studies.BillEtAl2025.georgian_da : ConjParticle

Georgian J particle

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.georgian_da = { language := "Georgian", form := "da", gloss := "and", role := "J", boundMorpheme := false }

def Phenomena.Coordination.Studies.BillEtAl2025.georgian_c : ConjParticle

Georgian MU particle (clitic)

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.georgian_c = { language := "Georgian", form := "-c", gloss := "MU/also", role := "MU", boundMorpheme := true }

def Phenomena.Coordination.Studies.BillEtAl2025.hungarian_es : ConjParticle

Hungarian J particle

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.hungarian_es = { language := "Hungarian", form := "és", gloss := "and", role := "J", boundMorpheme := false }

def Phenomena.Coordination.Studies.BillEtAl2025.hungarian_is : ConjParticle

Hungarian MU particle

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.hungarian_is = { language := "Hungarian", form := "is", gloss := "MU/also", role := "MU", boundMorpheme := false }

def Phenomena.Coordination.Studies.BillEtAl2025.georgianStrategies : List ConjunctionStrategy

Both Georgian and Hungarian allow all three strategies. This is typologically rare — most languages have only one or two.

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def Phenomena.Coordination.Studies.BillEtAl2025.hungarianStrategies : List ConjunctionStrategy

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theorem Phenomena.Coordination.Studies.BillEtAl2025.georgian_mu_bound : georgian_c.boundMorpheme = true

Key morphological difference: Georgian MU (-c) is a bound clitic, Hungarian MU (is) is a free morpheme. This may be relevant to the cross-linguistic difference in results (@cite{clark-2017}: free morphemes may be acquired more readily than bound).

theorem Phenomena.Coordination.Studies.BillEtAl2025.hungarian_mu_free : hungarian_is.boundMorpheme = false

inductive Phenomena.Coordination.Studies.BillEtAl2025.Group : Type

• adult : Group
• child : Group

instance Phenomena.Coordination.Studies.BillEtAl2025.instDecidableEqGroup : DecidableEq Group

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.instDecidableEqGroup x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Coordination.Studies.BillEtAl2025.instBEqGroup.beq : Group → Group → Bool

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.instBEqGroup.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Coordination.Studies.BillEtAl2025.instBEqGroup : BEq Group

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.instBEqGroup = { beq := Phenomena.Coordination.Studies.BillEtAl2025.instBEqGroup.beq }

instance Phenomena.Coordination.Studies.BillEtAl2025.instReprGroup : Repr Group

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.instReprGroup = { reprPrec := Phenomena.Coordination.Studies.BillEtAl2025.instReprGroup.repr }

def Phenomena.Coordination.Studies.BillEtAl2025.instReprGroup.repr : Group → ℕ → Std.Format

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structure Phenomena.Coordination.Studies.BillEtAl2025.AgeRange : Type

Age range for a participant group, in months.

• minMonths : ℕ
• maxMonths : ℕ
• meanMonths : ℕ

instance Phenomena.Coordination.Studies.BillEtAl2025.instReprAgeRange : Repr AgeRange

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.instReprAgeRange = { reprPrec := Phenomena.Coordination.Studies.BillEtAl2025.instReprAgeRange.repr }

def Phenomena.Coordination.Studies.BillEtAl2025.instReprAgeRange.repr : AgeRange → ℕ → Std.Format

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structure Phenomena.Coordination.Studies.BillEtAl2025.ParticipantGroup : Type

Participant group with demographics.

• language : String
• group : Group
• n : ℕ
• ageRange : Option AgeRange

def Phenomena.Coordination.Studies.BillEtAl2025.instReprParticipantGroup.repr : ParticipantGroup → ℕ → Std.Format

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instance Phenomena.Coordination.Studies.BillEtAl2025.instReprParticipantGroup : Repr ParticipantGroup

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.instReprParticipantGroup = { reprPrec := Phenomena.Coordination.Studies.BillEtAl2025.instReprParticipantGroup.repr }

def Phenomena.Coordination.Studies.BillEtAl2025.georgianChildren : ParticipantGroup

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def Phenomena.Coordination.Studies.BillEtAl2025.georgianAdults : ParticipantGroup

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.georgianAdults = { language := "Georgian", group := Phenomena.Coordination.Studies.BillEtAl2025.Group.adult, n := 41, ageRange := none }

def Phenomena.Coordination.Studies.BillEtAl2025.hungarianChildren : ParticipantGroup

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def Phenomena.Coordination.Studies.BillEtAl2025.hungarianAdults : ParticipantGroup

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.hungarianAdults = { language := "Hungarian", group := Phenomena.Coordination.Studies.BillEtAl2025.Group.adult, n := 30, ageRange := none }

def Phenomena.Coordination.Studies.BillEtAl2025.georgianAgeAccuracyCorrelation : Float

Age-accuracy correlation in Georgian children: medium positive. r(525) = 0.31, p < 0.001 (footnote 8).

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.georgianAgeAccuracyCorrelation = 0.31

def Phenomena.Coordination.Studies.BillEtAl2025.georgianAgeSentencePlayedCorrelation : Float

Age-sentencePlayedN correlation in Georgian children: small negative. r(497) = -0.18, p < 0.001 (footnote 9). Older children needed fewer replays.

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.georgianAgeSentencePlayedCorrelation = -0.18

structure Phenomena.Coordination.Studies.BillEtAl2025.ConditionResult : Type

A single cell in the Group × SentenceType design.

• language : String
• group : Group
• sentenceType : ConjunctionStrategy
• accuracyPct : ℕ

  Accuracy (percentage 0-100)

• nParticipants : ℕ

  Number of participants

instance Phenomena.Coordination.Studies.BillEtAl2025.instReprConditionResult : Repr ConditionResult

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.instReprConditionResult = { reprPrec := Phenomena.Coordination.Studies.BillEtAl2025.instReprConditionResult.repr }

def Phenomena.Coordination.Studies.BillEtAl2025.instReprConditionResult.repr : ConditionResult → ℕ → Std.Format

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def Phenomena.Coordination.Studies.BillEtAl2025.georgianAccuracy : List ConditionResult

Georgian accuracy data (approximate from Figure 4). Adults near ceiling across all conditions. Children lower but no significant sentence-type effect on accuracy.

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structure Phenomena.Coordination.Studies.BillEtAl2025.LRTResult : Type

Result of a Likelihood Ratio Test comparing nested models.

We encode statistical test results as data, not as theorems about the underlying population. A non-significant result means the test did not detect an effect — not that no effect exists.

• effect : String
• df : ℕ
• chiSquared : Float
• pValue : Float
• significant : Bool

  Whether p < .05 (conventional threshold)

instance Phenomena.Coordination.Studies.BillEtAl2025.instReprLRTResult : Repr LRTResult

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.instReprLRTResult = { reprPrec := Phenomena.Coordination.Studies.BillEtAl2025.instReprLRTResult.repr }

def Phenomena.Coordination.Studies.BillEtAl2025.instReprLRTResult.repr : LRTResult → ℕ → Std.Format

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def Phenomena.Coordination.Studies.BillEtAl2025.georgianAccuracyLRT : List LRTResult

Table 1: LRT results for Georgian accuracy.

Only group is significant — sentence-type effect NOT detected. NOTE: This is a null result. The act-out task allowed unlimited replays, which may have washed out accuracy differences (see Section 3.1.2).

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def Phenomena.Coordination.Studies.BillEtAl2025.georgianSentencePlayedLRT : List LRTResult

Table 2: LRT results for Georgian sentence-played-n.

All effects significant — this is where the key finding emerges.

Equations

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structure Phenomena.Coordination.Studies.BillEtAl2025.PairwiseComparison : Type

Pairwise comparison for sentence-played-n (Table 3). Tukey-adjusted p-values. Values on log scale, encoded as thousandths (e.g., -176 = -0.176) so that comparisons are decidable.

• group : Group
• contrast : String
• estimate_thou : ℤ

  Estimate on log scale, in thousandths (-176 = -0.176)

• se_thou : ℕ

  Standard error in thousandths

• df : ℕ
• tRatio_thou : ℤ

  t-ratio in thousandths

• pValue_tenThou : ℕ

  p-value in ten-thousandths (1 = 0.0001, 670 = 0.067)

• significant : Bool

def Phenomena.Coordination.Studies.BillEtAl2025.instReprPairwiseComparison.repr : PairwiseComparison → ℕ → Std.Format

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instance Phenomena.Coordination.Studies.BillEtAl2025.instReprPairwiseComparison : Repr PairwiseComparison

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.instReprPairwiseComparison = { reprPrec := Phenomena.Coordination.Studies.BillEtAl2025.instReprPairwiseComparison.repr }

def Phenomena.Coordination.Studies.BillEtAl2025.georgianChild_j_vs_jmu : PairwiseComparison

Georgian children: J vs J-MU (p < .0001). Negative = J-MU harder.

Equations

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def Phenomena.Coordination.Studies.BillEtAl2025.georgianChild_j_vs_mu : PairwiseComparison

Georgian children: J vs MU (p = .067, marginal).

Equations

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def Phenomena.Coordination.Studies.BillEtAl2025.georgianChild_jmu_vs_mu : PairwiseComparison

Georgian children: J-MU vs MU (p < .01). Positive = J-MU harder.

Equations

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def Phenomena.Coordination.Studies.BillEtAl2025.georgianChildPairwise : List PairwiseComparison

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def Phenomena.Coordination.Studies.BillEtAl2025.georgianAdultPairwise : List PairwiseComparison

Adults show no pairwise differences (all p > .6).

Equations

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def Phenomena.Coordination.Studies.BillEtAl2025.hungarianAccuracyLRT : List LRTResult

Table 4: LRT results for Hungarian accuracy.

No significant effects detected. NOTE: Null result — Hungarian children were somewhat older-behaving than Georgian children despite being younger (see fn. 4).

Equations

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def Phenomena.Coordination.Studies.BillEtAl2025.hungarianSentencePlayedLRT : List LRTResult

Table 5: LRT results for Hungarian sentence-played-n.

Only group significant — sentence-type effect NOT detected. NOTE: Null result for sentence-type. Could reflect: (a) no actual difference, (b) insufficient power (n=25 children), (c) Hungarian MU (free morpheme "is") being easier than Georgian MU (bound clitic "-c"), washing out complexity effects.

Equations

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theorem Phenomena.Coordination.Studies.BillEtAl2025.georgian_child_jmu_harder_than_j : georgianChild_j_vs_jmu.significant = true ∧ georgianChild_j_vs_jmu.estimate_thou < 0

Georgian children replayed J-MU sentences significantly more than J sentences.

This is the OPPOSITE of what @cite{mitrovic-sauerland-2016} + Transparency Principle predicts. The prediction was that J-MU (most transparent) should be EASIEST.

Negative estimate means J < J-MU in replay count (J-MU harder).

theorem Phenomena.Coordination.Studies.BillEtAl2025.georgian_child_jmu_harder_than_mu : georgianChild_jmu_vs_mu.significant = true ∧ georgianChild_jmu_vs_mu.estimate_thou > 0

Georgian children replayed J-MU sentences significantly more than MU sentences.

Positive estimate means J-MU > MU in replay count (J-MU harder).

theorem Phenomena.Coordination.Studies.BillEtAl2025.georgian_child_j_vs_mu_not_significant : georgianChild_j_vs_mu.significant = false

No significant difference between J and MU for Georgian children.

NOTE: This is a null result (p = .067, marginal). We record the non-significance but do NOT assert that J and MU are equally difficult.

def Phenomena.Coordination.Studies.BillEtAl2025.transparencyPredicts (s1 s2 : ConjunctionStrategy) : Bool

The Transparency Principle: Learning is easier for overt and unambiguous (1-to-1) form-meaning mappings than for covert and/or conflated (many-to-1) mappings.

Equations

• Phenomena.Coordination.Studies.BillEtAl2025.transparencyPredicts s1 s2 = decide (s1.overtMorphemeCount > s2.overtMorphemeCount)

theorem Phenomena.Coordination.Studies.BillEtAl2025.jmu_predicted_most_transparent : transparencyPredicts ConjunctionStrategy.jMu ConjunctionStrategy.jOnly = true ∧ transparencyPredicts ConjunctionStrategy.jMu ConjunctionStrategy.muOnly = true

@cite{mitrovic-sauerland-2016} + Transparency Principle predicts J-MU is more transparent than both J-only and MU-only.

theorem Phenomena.Coordination.Studies.BillEtAl2025.georgian_contradicts_transparency : transparencyPredicts ConjunctionStrategy.jMu ConjunctionStrategy.jOnly = true ∧ georgianChild_j_vs_jmu.estimate_thou < 0

The Georgian sentence-played-n data contradicts this prediction: J-MU was HARDER (more replays), not easier. The significant pairwise comparisons go in the wrong direction.

Link to Phenomena/Gradability/Imprecision/FormMeaning.lean

The Transparency Principle is the acquisition-side counterpart of the No Needless Manner Violations principle formalized in FormMeaning.lean.

Both principles relate form complexity to meaning:

• NNMV: More complex form → more precise meaning
• Transparency: More overt form-meaning mapping → easier acquisition

The andBoth datum in FormMeaning.lean is particularly relevant: "Ann and Bert" (J-only) vs "both Ann and Bert" (≈ J+MU). "Both" adds precision (removes homogeneity gap) — it's arguably an overt realization of MU/distributivity, paralleling the J-MU strategy.

Bill et al.'s finding complicates this picture: in Georgian, adding overt MU+J (maximum transparency) made comprehension HARDER, suggesting that morphological complexity can outweigh transparency benefits.

Link to Phenomena/AdditiveParticles/Data.lean

Japanese "mo" (listed as an additive particle in AdditiveParticles/Data.lean) is the canonical MU particle in Mitrović & Sauerland's framework. In conjunction, "mo...mo" = MU-only strategy:

Taroo-mo Hanako-mo neta Taro-MU Hanako-MU slept "Both Taro and Hanako slept"

Similarly, Hungarian "is" and Georgian "-c" serve as both additive particles and conjunction MU particles — unifying two phenomena under a single morpheme.

Semantic Decomposition (@cite{mitrovic-sauerland-2016})

The M&S decomposition maps onto three operations already formalized:

M&S piece	Semantic operation	Montague/Conjunction.lean
J	Set intersection	genConj at ⟨⟨e,t⟩,⟨⟨e,t⟩,t⟩⟩
MU	Subset (INCL)	inclFunc / inclProperty
☉	{x} formation	typeRaise (e → ⟨⟨e,t⟩,t⟩)

The full derivation of "Mary and Susan sleep":

1. ☉(Mary) = λP.P(Mary) — typeRaise
2. MU(☉(Mary), sleep) = {Mary} ⊆ ⟦sleep⟧ — inclFunc
3. Similarly for Susan
4. J combines the two MU-results via conjunction — genConj at type t

The result: {Mary} ⊆ ⟦sleep⟧ ∧ {Susan} ⊆ ⟦sleep⟧ = sleep(Mary) ∧ sleep(Susan)

theorem Phenomena.Coordination.Studies.BillEtAl2025.typeRaise_incl_reduces {m : Semantics.Montague.Model} (e : m.Entity) (p : m.Entity → Bool) : Semantics.Montague.Conjunction.typeRaise e p = p e

Type-raising an entity and checking subset inclusion of its singleton is equivalent to applying the predicate directly.

This is the core of the M&S decomposition: the roundtrip through ☉ + MU + J recovers ordinary conjunction semantics.

theorem Phenomena.Coordination.Studies.BillEtAl2025.ms_decomposition_eq_coord {m : Semantics.Montague.Model} (e1 e2 : m.Entity) (p : m.Entity → Bool) : (Semantics.Montague.Conjunction.typeRaise e1 p && Semantics.Montague.Conjunction.typeRaise e2 p) = Semantics.Montague.Conjunction.coordEntities e1 e2 p

Full M&S derivation: "DP₁ and DP₂ VP" via ☉ + MU + J yields the same result as Partee & Rooth's coordEntities.