Goldberg and Shirtz (2025): The English Phrase-as-Lemma Construction

This file formalizes Goldberg and Shirtz's phrase-as-lemma (PAL) construction: a phrase used in a slot reserved for a word ("a trickle-down policy", "the 'both sides do it' argument"), whose lemma-like construal presents the situation type as familiar to speaker and addressee, with wit and sarcasm as rhetorical effects of discussing the presumed familiar. Five preregistered forced-choice surveys found PAL sentences judged to imply more common knowledge than close paraphrases, and to be wittier and more sarcastic, robustly to PAL frequency, and found four narrowly defined subtypes (must-V, a simple ⟨PAL⟩, Don't ⟨PAL⟩ me, the old ⟨PAL⟩ N) judged more natural than minimally different foils.

The paper's Figure 5 network is a Constructicon (figure5): the prenominal PAL construction inherits in normal mode from both the NN compound and adjectival modification, which conflict on whether the output is a word and on stress (mothers_conflict), so PAL states exactly those properties and inherits the rest (inherited_palN). The zero-level PAL and the four conventional subtypes are joined to it by motivation links, and removing PAL leaves a phrase in a word slot unlicensed (pal_load_bearing). The attested tokens of example (1) and Tables 2–3 and the comparable constructions of section 7 are rows: PALs occupy every word-class slot and take that slot's inflection (rows_inflection), and the host frame of a comparable construction need not be a compound (hostFrames_complete).

Implementation notes

Only the two thick arrows of Figure 5 are inheritance links; its thin two-headed arrows are motivation links, which pass no information down. The experimental statistics stay in the paper. The lemma-like familiarity is recorded as not-at-issue content, although the paper treats it as an invited construal that speakers exploit precisely for situation types that are not antecedently familiar.

References

• [GS25]
• [Gol95]
• [Mei07]
• [TK15]
• [Sag12]

The Figure 5 constructicon

def GoldbergShirtz2025.palConstruction : ConstructionGrammar.Construction Unit

In the prenominal PAL construction a zero-level PAL whose internal syntax is phrasal modifies a head N, forming an N′ (the paper's structure (7), [N′ PAL⁰ N], vs. the NN compound's [N⁰ N⁰ N⁰]). Whether the head N is a word is left underspecified since PALs may modify nouns with complements ("a 'don't mess with me' type of driver").

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def GoldbergShirtz2025.mustVerbConstruction : ConstructionGrammar.Construction Unit

The semiproductive must-V subtype, frequently instantiated by must-read, must-see, must-have. Study 5 tested only rare tokens (≤ 10 COCA hits) against should-V foils.

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def GoldbergShirtz2025.aSimplePALConstruction : ConstructionGrammar.Construction Unit

In the a simple ⟨PAL⟩ subtype the PAL is itself the head noun, with simple marking the situation type as routine ("Could've tried a simple 'I'm sorry.'"). Study 5's foils used a short.

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def GoldbergShirtz2025.dontPALmeConstruction : ConstructionGrammar.Construction Unit

In the Don't ⟨PAL⟩ me subtype the PAL fills a V slot, must quote the immediately preceding discourse, and occurs in an interdiction context (A says "you're welcome", B replies "No, don't 'you're welcome' me."). Study 5's foils broke exactly the quote-from-context or interdiction condition.

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def GoldbergShirtz2025.theOldPALConstruction : ConstructionGrammar.Construction Unit

The the old ⟨PAL⟩ (N) subtype, with optional head N and old marking the situation type as conventional ("my dad pulled the old 'I'm going to the store for smokes, be back in five'"). Study 5's foils used the tired.

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def GoldbergShirtz2025.nnCompound : ConstructionGrammar.Construction Unit

The NN compound construction is a parent of PAL, passing down internal stress and a tight unit.

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def GoldbergShirtz2025.adjNModification : ConstructionGrammar.Construction Unit

The adjectival modification construction is a parent of PAL, passing down the prenominal slot.

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Degrees of abstraction (Table 8)

def GoldbergShirtz2025.veggieWrapForm : ConstructionGrammar.TypedForm String

Veggie-wrap, a fully lexically specified noun compound (the top row of Table 8).

Equations

• GoldbergShirtz2025.veggieWrapForm = [{ filler := ConstructionGrammar.SlotFiller.fixed "veggie" }, { filler := ConstructionGrammar.SlotFiller.fixed "wrap", isHead := true }]

theorem GoldbergShirtz2025.table8_specificity : ConstructionGrammar.derivedSpecificity veggieWrapForm = ConstructionGrammar.Specificity.lexicallySpecified ∧ aSimplePALConstruction.specificity = ConstructionGrammar.Specificity.partiallyOpen ∧ nnCompound.specificity = ConstructionGrammar.Specificity.fullyAbstract ∧ palConstruction.specificity = ConstructionGrammar.Specificity.fullyAbstract

The constructicon witnesses Table 8's degree-of-abstraction grid, in which veggie-wrap is lexically specified, a simple ⟨PAL⟩ partially open, and the NN-compound and prenominal-PAL schemas fully open and abstract.

def GoldbergShirtz2025.zeroLevelPAL : ConstructionGrammar.Construction Unit

The zero-level PAL, a phrase in a word-level position, with its familiar tokens (do-it-yourself, know-it-all, pay-as-you-go).

Equations

• GoldbergShirtz2025.zeroLevelPAL = { form := [{ filler := ConstructionGrammar.SlotFiller.phrasal, lex := some true }], meaning := (), pragmaticPoint := true }

inductive GoldbergShirtz2025.Figure5 : Type

The constructions of Figure 5.

• nnCompound : Figure5

  The NN compound, N⁰ modifies N⁰.

• adjN : Figure5

  Adjectival modification, Adj modifies N′.

• palN : Figure5

  The prenominal PAL construction, PAL⁰ modifies N, at the center of the figure.

• pal : Figure5

  The zero-level PAL.

• mustV : Figure5

  must-V.

• aSimple : Figure5

  a simple ⟨PAL⟩.

• dontMe : Figure5

  Don't ⟨PAL⟩ me.

• theOld : Figure5

  the old ⟨PAL⟩ (N).

@[instance_reducible]

instance GoldbergShirtz2025.instDecidableEqFigure5 : DecidableEq Figure5

Equations

• GoldbergShirtz2025.instDecidableEqFigure5 x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance GoldbergShirtz2025.instFintypeFigure5 : Fintype Figure5

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def GoldbergShirtz2025.construction : Figure5 → ConstructionGrammar.Construction Unit

The construction at each node of Figure 5.

Equations

• GoldbergShirtz2025.construction GoldbergShirtz2025.Figure5.nnCompound = GoldbergShirtz2025.nnCompound
• GoldbergShirtz2025.construction GoldbergShirtz2025.Figure5.adjN = GoldbergShirtz2025.adjNModification
• GoldbergShirtz2025.construction GoldbergShirtz2025.Figure5.palN = GoldbergShirtz2025.palConstruction
• GoldbergShirtz2025.construction GoldbergShirtz2025.Figure5.pal = GoldbergShirtz2025.zeroLevelPAL
• GoldbergShirtz2025.construction GoldbergShirtz2025.Figure5.mustV = GoldbergShirtz2025.mustVerbConstruction
• GoldbergShirtz2025.construction GoldbergShirtz2025.Figure5.aSimple = GoldbergShirtz2025.aSimplePALConstruction
• GoldbergShirtz2025.construction GoldbergShirtz2025.Figure5.dontMe = GoldbergShirtz2025.dontPALmeConstruction
• GoldbergShirtz2025.construction GoldbergShirtz2025.Figure5.theOld = GoldbergShirtz2025.theOldPALConstruction

def GoldbergShirtz2025.figure5 : ConstructionGrammar.Constructicon Figure5 Unit

Figure 5. The prenominal PAL construction inherits in normal mode from the NN compound and from adjectival modification, the two thick arrows. The zero-level PAL and the conventional subtypes are joined to it by the thin two-headed arrows, must-V and Don't ⟨PAL⟩ me through the zero-level PAL; these motivate the subtypes and pass no information down. The caption calls the arrows "motivation and (normal mode) inheritance links" and assigns none of the link types of [Gol95].

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def GoldbergShirtz2025.Figure5.rank : Figure5 → ℕ

The depth of a construction below those it inherits from.

Equations

• GoldbergShirtz2025.Figure5.palN.rank = 1
• x✝.rank = 0

@[instance_reducible]

instance GoldbergShirtz2025.instPartialOrderFigure5 : PartialOrder Figure5

Equations

• GoldbergShirtz2025.instPartialOrderFigure5 = GoldbergShirtz2025.figure5.partialOrder GoldbergShirtz2025.Figure5.rank GoldbergShirtz2025.instPartialOrderFigure5._proof_1

@[instance_reducible]

instance GoldbergShirtz2025.instDecidableLEFigure5 : DecidableLE Figure5

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theorem GoldbergShirtz2025.isMother_iff (c m : Figure5) : figure5.IsMother c m ↔ c = Figure5.palN ∧ (m = Figure5.nnCompound ∨ m = Figure5.adjN)

Only the prenominal PAL construction inherits, from the NN compound and adjectival modification.

Two mothers force normal-mode inheritance (§6)

The form-side properties at issue in Figure 5, each stated by the constructions that specify it and inherited by DefaultInheritance.inherited over the network's order. PAL N's two mothers conflict, the NN compound yielding an N⁰ with stress within the modifier and adjectival modification an N′ with head stress, so were PAL N to state neither property it would inherit both values of each (mothers_conflict): "specifications in two mother nodes may conflict with one another", which makes complete inheritance "unsuitable whenever a node is allowed more than a single mother". PAL N states exactly those two properties, and inherits the rest (inherited_palN).

inductive GoldbergShirtz2025.StressLocus : Type

The locus of primary stress in a modification construction is within the modifier for compound stress (BLACKbird) and on the head for phrasal modification (black BIRD).

• modifier : StressLocus
• head : StressLocus

@[instance_reducible]

instance GoldbergShirtz2025.instDecidableEqStressLocus : DecidableEq StressLocus

Equations

• GoldbergShirtz2025.instDecidableEqStressLocus x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def GoldbergShirtz2025.instReprStressLocus.repr : StressLocus → ℕ → Std.Format

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@[instance_reducible]

instance GoldbergShirtz2025.instReprStressLocus : Repr StressLocus

Equations

• GoldbergShirtz2025.instReprStressLocus = { reprPrec := GoldbergShirtz2025.instReprStressLocus.repr }

inductive GoldbergShirtz2025.ModPosition : Type

Position of the modifier slot relative to the head.

• prenominal : ModPosition
• postnominal : ModPosition

@[instance_reducible]

instance GoldbergShirtz2025.instDecidableEqModPosition : DecidableEq ModPosition

Equations

• GoldbergShirtz2025.instDecidableEqModPosition x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def GoldbergShirtz2025.instReprModPosition.repr : ModPosition → ℕ → Std.Format

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@[instance_reducible]

instance GoldbergShirtz2025.instReprModPosition : Repr ModPosition

Equations

• GoldbergShirtz2025.instReprModPosition = { reprPrec := GoldbergShirtz2025.instReprModPosition.repr }

inductive GoldbergShirtz2025.SelfEmbedding : Type

Whether a construction's output can recur inside the construction's own open slot.

• allowed : SelfEmbedding
• banned : SelfEmbedding

@[instance_reducible]

instance GoldbergShirtz2025.instDecidableEqSelfEmbedding : DecidableEq SelfEmbedding

Equations

• GoldbergShirtz2025.instDecidableEqSelfEmbedding x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance GoldbergShirtz2025.instReprSelfEmbedding : Repr SelfEmbedding

Equations

• GoldbergShirtz2025.instReprSelfEmbedding = { reprPrec := GoldbergShirtz2025.instReprSelfEmbedding.repr }

def GoldbergShirtz2025.instReprSelfEmbedding.repr : SelfEmbedding → ℕ → Std.Format

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def GoldbergShirtz2025.lex : Figure5 → Option Bool

A construction may state whether its output is a word. PAL N forms an N′, a phrase, with adjectival modification and against the compound's N⁰, a word.

Equations

• GoldbergShirtz2025.lex GoldbergShirtz2025.Figure5.nnCompound = some true
• GoldbergShirtz2025.lex GoldbergShirtz2025.Figure5.adjN = some false
• GoldbergShirtz2025.lex GoldbergShirtz2025.Figure5.palN = some false
• GoldbergShirtz2025.lex x✝ = none

def GoldbergShirtz2025.modPosition : Figure5 → Option ModPosition

The position of the modifier slot, which both mothers state and PAL N does not.

Equations

• GoldbergShirtz2025.modPosition GoldbergShirtz2025.Figure5.nnCompound = some GoldbergShirtz2025.ModPosition.prenominal
• GoldbergShirtz2025.modPosition GoldbergShirtz2025.Figure5.adjN = some GoldbergShirtz2025.ModPosition.prenominal
• GoldbergShirtz2025.modPosition x✝ = none

def GoldbergShirtz2025.stress : Figure5 → Option StressLocus

A construction may state the locus of primary stress. PAL N forms "a tight semantic and phonological unit", with the stress within the PAL as in the compound, against adjectival modification.

Equations

• GoldbergShirtz2025.stress GoldbergShirtz2025.Figure5.nnCompound = some GoldbergShirtz2025.StressLocus.modifier
• GoldbergShirtz2025.stress GoldbergShirtz2025.Figure5.palN = some GoldbergShirtz2025.StressLocus.modifier
• GoldbergShirtz2025.stress GoldbergShirtz2025.Figure5.adjN = some GoldbergShirtz2025.StressLocus.head
• GoldbergShirtz2025.stress x✝ = none

def GoldbergShirtz2025.selfEmbedding : Figure5 → Option SelfEmbedding

A construction may state whether its output self-embeds. Adjectival modification bans it, and "like Adj + N combinations, the PAL N construction cannot be recursively embedded within another PAL N construction".

Equations

• GoldbergShirtz2025.selfEmbedding GoldbergShirtz2025.Figure5.adjN = some GoldbergShirtz2025.SelfEmbedding.banned
• GoldbergShirtz2025.selfEmbedding x✝ = none

theorem GoldbergShirtz2025.mothers_conflict : DefaultInheritance.inherited (Function.update lex Figure5.palN none) Figure5.palN = {true, false} ∧ DefaultInheritance.inherited (Function.update stress Figure5.palN none) Figure5.palN = {StressLocus.modifier, StressLocus.head}

Were PAL N to state neither whether its output is a word nor its stress, it would inherit both mothers' values of each.

theorem GoldbergShirtz2025.inherited_palN : DefaultInheritance.inherited lex Figure5.palN = {false} ∧ DefaultInheritance.inherited modPosition Figure5.palN = {ModPosition.prenominal} ∧ DefaultInheritance.inherited stress Figure5.palN = {StressLocus.modifier} ∧ DefaultInheritance.inherited selfEmbedding Figure5.palN = {SelfEmbedding.banned}

Normal-mode inheritance computes PAL N's full specification, its own phrasal N′ and stress within the modifier, the prenominal slot from both mothers, which agree, and non-self-embedding from adjectival modification.

Licensing: PAL is load-bearing

A minimal demonstration with the licensing relation (Licenses): the attested "a must-do task" (the paper's ex. (1b), determiner elided) parses as a phrase-daughter in the modifier slot plus a head noun. The constructions of Figure 5 license it through the PAL construction, and without PAL it is rejected: the phrase-in-word-slot configuration has no other license.

def GoldbergShirtz2025.mustVCore : ConstructionGrammar.Construction Unit

The internal syntax of the must-do PAL, must-V (cf. mustVerbConstruction, which is the full prenominal construction).

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def GoldbergShirtz2025.demoInventory : List (ConstructionGrammar.Construction Unit)

The constructions of Figure 5 and the must-V-internal construction.

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def GoldbergShirtz2025.mustDoTask : PhraseStructure.Tree Unit Morphology.Word

In "must-do task" (ex. (1b), determiner elided) the PAL phrase is a constituent daughter in the word-level modifier slot.

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theorem GoldbergShirtz2025.demo_licenses_mustDoTask : ConstructionGrammar.Licenses demoInventory mustDoTask

The inventory licenses the PAL token.

theorem GoldbergShirtz2025.pal_load_bearing : ¬ConstructionGrammar.Licenses (demoInventory.erase palConstruction) mustDoTask

Without the PAL construction the token is rejected, since nothing else licenses a phrase in a word-level modifier slot. PAL is load-bearing.

def GoldbergShirtz2025.palMeaning (W : Type u_1) (situationType headNoun : W → Prop) : ConventionalImplicature.TwoDim W (W → Prop)

A PAL utterance has a two-part meaning. The head noun's denotation is at-issue (an instance of the situation type), and the lemma-like construal contributes, as not-at-issue content, that the situation type itself is presumed familiar ("presumes familiarity with 'PAL'", Figure 5).

The paper treats the familiarity as an invited as-if construal rather than a hard definedness condition. Speakers exploit the construction precisely for situation types that are not antecedently familiar (observational humor, sniglets), so common-ground satisfaction is typically reached by accommodation or pretense, not antecedent entailment.

Equations

• GoldbergShirtz2025.palMeaning W situationType headNoun = { atIssue := headNoun, notAtIssue := situationType }

Irreducibility

theorem GoldbergShirtz2025.pal_irreducible : ¬palConstruction.IsFullyCompositional

The PAL construction is not fully compositional. Pairing phrase-in-a-word-slot form with a presumed-familiarity function is a construction-specific pragmatic function, so PAL cannot be decomposed into the three universal combination schemata (see Construction.IsFullyCompositional).

theorem GoldbergShirtz2025.pal_form_phrase_in_word_slot : ∃ s ∈ palConstruction.form, s.IsPhraseInWordSlot

The PAL modifier slot is a phrase in a word-level position — the typed content of "phrase-as-lemma". The NN compound's modifier slot is the minimal contrast, with the same zero-level position and a word filler.

Attested tokens

PALs prototypically modify nouns but occur as head nouns, predicative adjectives, and verbs (Table 2), and take the word-level inflection of the slot they fill (Table 3).

inductive GoldbergShirtz2025.PALPosition : Type

The word-class slot a PAL fills.

• prenominalModifier : PALPosition
• headNoun : PALPosition
• predicativeAdjective : PALPosition
• verb : PALPosition

@[instance_reducible]

instance GoldbergShirtz2025.instDecidableEqPALPosition : DecidableEq PALPosition

Equations

• GoldbergShirtz2025.instDecidableEqPALPosition x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance GoldbergShirtz2025.instFintypePALPosition : Fintype PALPosition

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inductive GoldbergShirtz2025.Inflection : Type

Word-level inflection attested on a PAL.

• plural : Inflection
• agentivePlural : Inflection
• gerund : Inflection

@[instance_reducible]

instance GoldbergShirtz2025.instDecidableEqInflection : DecidableEq Inflection

Equations

• GoldbergShirtz2025.instDecidableEqInflection x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def GoldbergShirtz2025.Inflection.position : Inflection → PALPosition

An affix is the inflection of a slot, nominal for the plural and agentive -er and verbal for -ing.

Equations

• GoldbergShirtz2025.Inflection.plural.position = GoldbergShirtz2025.PALPosition.headNoun
• GoldbergShirtz2025.Inflection.agentivePlural.position = GoldbergShirtz2025.PALPosition.headNoun
• GoldbergShirtz2025.Inflection.gerund.position = GoldbergShirtz2025.PALPosition.verb

structure GoldbergShirtz2025.Row : Type

An attested English PAL records its slot and any inflection it carries.

• position : PALPosition
• inflection : Option Inflection

@[instance_reducible]

instance GoldbergShirtz2025.instDecidableEqRow : DecidableEq Row

Equations

• GoldbergShirtz2025.instDecidableEqRow = GoldbergShirtz2025.instDecidableEqRow.decEq

def GoldbergShirtz2025.instDecidableEqRow.decEq (x✝ x✝¹ : Row) : Decidable (x✝ = x✝¹)

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def GoldbergShirtz2025.Row.ofDatum (ex : Datum) : Option Row

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def GoldbergShirtz2025.rows : List Row

The English tokens of (1a)–(1c), Table 2, and Table 3.

Equations

• GoldbergShirtz2025.rows = List.filterMap GoldbergShirtz2025.Row.ofDatum GoldbergShirtz2025.Examples.all

theorem GoldbergShirtz2025.rows_position (p : PALPosition) : ∃ r ∈ rows, r.position = p

PALs are attested in every word-class slot (Table 2).

theorem GoldbergShirtz2025.rows_inflection (r : Row) : r ∈ rows → ∀ i ∈ r.inflection, i.position = r.position

A PAL takes the inflection of the slot it fills (Table 3).

Comparable constructions in other languages (section 7)

inductive GoldbergShirtz2025.PALHostFrame : Type

A comparable construction is hosted by a compound(-like) frame in West Germanic and Turkish, where the compound marker sits on the head noun, or the complement of a preposition in Hebrew and Brazilian Portuguese.

• compound : PALHostFrame
• prepositionComplement : PALHostFrame

@[instance_reducible]

instance GoldbergShirtz2025.instDecidableEqPALHostFrame : DecidableEq PALHostFrame

Equations

• GoldbergShirtz2025.instDecidableEqPALHostFrame x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance GoldbergShirtz2025.instFintypePALHostFrame : Fintype PALHostFrame

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def GoldbergShirtz2025.hostFrames : List PALHostFrame

The host frames of the German, Dutch, Afrikaans, Turkish, Hebrew, and Brazilian Portuguese PALs of (8) and (15)–(18).

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theorem GoldbergShirtz2025.hostFrames_complete (f : PALHostFrame) : f ∈ hostFrames

A PAL need not resemble a compound; it need only fill a slot typical of single words, so both host frames are attested.