@cite{goldberg-shirtz-2025}: PAL Constructions — Theoretical Analysis

@cite{goldberg-shirtz-2025}

Formalizes the PAL (Phrasal Adjective-Like) construction and its inheritance network using Construction Grammar types from ConstructionGrammar.Basic.

PALs are phrases that fill word-level syntactic slots (e.g., "a grab-and-go lunch", "a must-see movie"). Their key theoretical properties:

1. Form motivates function: A phrase in a word slot gets lemma-like interpretation — the PAL names a situation type rather than describing it.
2. Familiarity presupposition: PALs presuppose the situation type is in the common ground (Studies 1a/1b).
3. Two-dimensional meaning: At-issue content (head noun denotation) + CI content (social signaling: wit, sarcasm).
4. Inheritance network: PALs inherit from both NN compounds (stress, no plural on modifier) and Adj+N constructions (prenominal position).

Section 1: PAL Construction definitions

def ConstructionGrammar.Studies.GoldbergShirtz2025.palConstruction : Construction

The PAL construction: a phrase fills a word-level modifier slot.

Form: [N' PAL⁰ N] — a phrasal expression occupies a head/modifier position that normally expects a single word.

Meaning: The PAL names a familiar situation type, presupposing shared knowledge of that type.

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def ConstructionGrammar.Studies.GoldbergShirtz2025.mustVerbConstruction : Construction

must-VERB subtype: "a must-see movie", "a must-read book".

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def ConstructionGrammar.Studies.GoldbergShirtz2025.aSimplePALConstruction : Construction

a simple ⟨PAL⟩ subtype: "a simple meet-and-greet".

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def ConstructionGrammar.Studies.GoldbergShirtz2025.dontPALmeConstruction : Construction

Don't PAL me: "Don't wink-wink me".

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def ConstructionGrammar.Studies.GoldbergShirtz2025.theOldPALConstruction : Construction

the old ⟨PAL⟩ N: "the old bait-and-switch trick".

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def ConstructionGrammar.Studies.GoldbergShirtz2025.nnCompound : Construction

NN compound construction (parent of PAL for stress/morphology).

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def ConstructionGrammar.Studies.GoldbergShirtz2025.adjNModification : Construction

Adjective + Noun modification construction (parent for position).

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Inheritance network (Figure 5 of @cite{goldberg-shirtz-2025})

def ConstructionGrammar.Studies.GoldbergShirtz2025.palConstructicon : Constructicon

The PAL constructicon: constructions + inheritance links.

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Section 2: Presupposition bridge

Connect PAL's familiarity presupposition to Core.Presupposition and Core.CommonGround infrastructure.

def ConstructionGrammar.Studies.GoldbergShirtz2025.palPresupposition (W : Type u_1) (situationType : BProp W) : Core.Presupposition.PrProp W

PAL presupposes the situation type is in the common ground.

The presupposition is the situation type proposition itself: if the PAL is "grab-and-go", the presupposition is that grab-and-go situations are a recognized category for both speaker and addressee.

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• ConstructionGrammar.Studies.GoldbergShirtz2025.palPresupposition W situationType = { presup := situationType, assertion := fun (x : W) => true }

def ConstructionGrammar.Studies.GoldbergShirtz2025.palTwoDim (W : Type u_1) (atIssue familiar : BProp W) : Semantics.Lexical.Expressives.TwoDimProp W

PAL two-dimensional meaning (@cite{potts-2005} two-dimensional semantics).

• At-issue: the head noun's denotation (e.g., "lunch" in "grab-and-go lunch")
• CI: speaker presupposes shared familiarity with the situation type

This connects PAL semantics to the existing TwoDimProp from Semantics.Lexical.Expressives.Basic.

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• ConstructionGrammar.Studies.GoldbergShirtz2025.palTwoDim W atIssue familiar = { atIssue := atIssue, ci := familiar }

theorem ConstructionGrammar.Studies.GoldbergShirtz2025.pal_presup_satisfied_by_cg (W : Type u_1) (situationType : BProp W) (c : Core.CommonGround.ContextSet W) (h : c ⊧ situationType) (w : W) : c w → (palPresupposition W situationType).presup w = true

When the situation type is in the common ground, the PAL's presupposition is satisfied.

theorem ConstructionGrammar.Studies.GoldbergShirtz2025.pal_ci_projects_through_neg (W : Type u_1) (atIssue familiar : BProp W) : (palTwoDim W atIssue familiar).neg.ci = familiar

PAL CI projects through negation (inherits from TwoDimProp).

"It's not a grab-and-go lunch" still conveys familiarity with grab-and-go.

Section 3: Core theoretical claims

State the paper's central claims as propositions. These connect the empirical data (in Phenomena/) to the theoretical analysis.

def ConstructionGrammar.Studies.GoldbergShirtz2025.claim_form_motivates_function : Prop

Claim 1: PAL form motivates PAL function.

A phrase filling a word-level slot gets lemma-like interpretation: the PAL names a situation type rather than compositionally describing it. This is a form-function correlation at the heart of CxG.

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theorem ConstructionGrammar.Studies.GoldbergShirtz2025.claim_form_motivates_function_holds : claim_form_motivates_function

Claim 1 holds by construction.

def ConstructionGrammar.Studies.GoldbergShirtz2025.claim_pal_presupposes_familiarity : Prop

Claim 2: PALs presuppose the situation type is common knowledge.

Supported by Studies 1a (common knowledge) and 1b (shared background): PALs are preferred when the situation type is mutually known.

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theorem ConstructionGrammar.Studies.GoldbergShirtz2025.claim_pal_presupposes_familiarity_holds : claim_pal_presupposes_familiarity

Claim 2 holds by definition of palPresupposition.