Purver & Ginzburg (2004): Clarifying Noun Phrase Semantics

[PG04]

[PG04] use fragment-reprise clarification data to constrain admissible NP denotations. The empirical lever is the Reprise Content Hypothesis (RCH): a fragment reprise question must query the standard semantic content of the fragment being reprised. Anything a theory says about NP denotation has to survive this test.

The empirical contrast

A: Jo arrived yesterday. B: Jo? A: A thief broke in last night. B: A thief?

Both responses are reprise fragments. The first naturally queries identity ("who is Jo?"); the second cannot — it queries the property ("someone you believe to be a thief?") rather than identity ("which specific thief?"). The asymmetry tracks the referential / non-referential distinction on the host NP, not its surface form.

The argument against generalized-quantifier denotations

Standard generalized-quantifier theory assigns a thief the denotation λP. ∃x. thief(x) ∧ P(x) of type (e → t) → t. A reprise of this fragment, if it queried the standard semantic content, would query at this functional type — but no observed reprise ever does. The empirical record only shows queries at individual or property type.

[PG04] resolve this by splitting the sign's contextual parameters into two fields:

• dgb-params: referential entities, anchored against context
• q-params: existentially-bound indices, closed at proposition level

Both have the same record-type shape — record entries with INDEX and RESTR(ICTION). The split lives at the sign level: 'Jo' contributes a dgb-params entry; 'a thief' contributes a q-params entry. Reprises operate on the q-params record, not on a higher-order GQ denotation. RCH then does hold under this revised account.

What this file proves

Two theorems about RCH (defined in Pragmatics/Dialogue/Gameboard/RepriseContent.lean):

1. gq_reprise_type_mismatch: a predictor that licenses only .functional queries — the GQ prediction — fails Weak RCH against any reprise event whose observed content includes .individual or .property queries.

2. qparams_split_satisfies_weakRCH: the predictor derived from the q-params/dgb-params split (qParamsPredictor) satisfies Weak RCH by construction.

Both theorems take a RepriseEvent carrying a host LocProp; the LocProp's new qcparams field (added in Gameboard/Basic.lean) is what makes the q-params record visible at the reprise interface.

def PurverGinzburg2004.aThiefSub : Discourse.Gameboard.SubUtterance

Sub-utterance 'a thief'.

Equations

• PurverGinzburg2004.aThiefSub = { phon := "a thief", cat := "NP", cont := "thief" }

def PurverGinzburg2004.aThiefBrokeIn : Discourse.Gameboard.LocProp String

Host LocProp for "A thief broke in last night." The non-referential 'a thief' contributes a q-param [x:IND, restr:thief(x)] via the sign-level architecture in Grammar.lean.

Equations

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

def PurverGinzburg2004.aThiefReprise : Discourse.Gameboard.RepriseEvent String

The intended-content reprise of 'a thief' in this host.

Equations

• PurverGinzburg2004.aThiefReprise = { host := PurverGinzburg2004.aThiefBrokeIn, sub := PurverGinzburg2004.aThiefSub, reading := Discourse.Gameboard.RFReading.intendedContent }

def PurverGinzburg2004.gqPredictor : Discourse.Gameboard.RchPredictor String

The generalized-quantifier predictor ([PG04] target): licenses only .functional-typed queries, since GQ denotations have type (e → t) → t. Stated as a predictor for empirical refutation.

Equations

• PurverGinzburg2004.gqPredictor x✝ = [Discourse.Gameboard.QueryType.functional]

theorem PurverGinzburg2004.aThief_reprise_observes_individual : Discourse.Gameboard.QueryType.individual ∈ Discourse.Gameboard.reprisedContent aThiefReprise.host aThiefReprise.sub aThiefReprise.reading

The observed reprise content for 'a thief' under intended-content reading includes an .individual query — querying the witness of the existential.

theorem PurverGinzburg2004.gqPredictor_licenses_only_functional (ev : Discourse.Gameboard.RepriseEvent String) : gqPredictor ev = [Discourse.Gameboard.QueryType.functional]

The GQ predictor licenses only .functional queries — no .individual.

theorem PurverGinzburg2004.individual_not_in_gqPredictor (ev : Discourse.Gameboard.RepriseEvent String) : Discourse.Gameboard.QueryType.individual ∉ gqPredictor ev

.individual is not in the GQ predictor's licensed set for any event.

theorem PurverGinzburg2004.gq_reprise_type_mismatch : ¬Discourse.Gameboard.WeakRCH gqPredictor

Type-mismatch theorem ([PG04], [Gin12] §8.5.1): the GQ predictor fails Weak RCH. Empirically, fragment reprises of indefinite NPs query at individual (and property) type; the GQ denotation predicts queries only at functional type. The two sets are disjoint, so even Weak RCH (observed ⊆ predicted) fails.

Witness: the 'a thief' / 'A thief?' reprise event constructed above.

theorem PurverGinzburg2004.qparams_split_satisfies_weakRCH : Discourse.Gameboard.WeakRCH Discourse.Gameboard.qParamsPredictor

The constructive alternative satisfies Weak RCH by construction.

[PG04]'s revision routes 'a thief'-style indefinites through the qcparams channel on the LocProp. The qParamsPredictor licenses exactly the queries that reprisedContent reports — every observed query is predicted, so Weak RCH holds. (Inherited from qParamsPredictor_satisfies_weakRCH in Gameboard/RepriseContent.lean; restated here for the empirical paper context.)

def PurverGinzburg2004.joSub : Discourse.Gameboard.SubUtterance

Sub-utterance 'Jo'.

Equations

• PurverGinzburg2004.joSub = { phon := "Jo", cat := "PROPN", cont := "jo" }

def PurverGinzburg2004.joArrived : Discourse.Gameboard.LocProp String

Host LocProp for "Jo arrived yesterday." 'Jo' is referential — contributes a cparams entry, not qcparams. Its reprise queries identity, not property.

Equations

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

theorem PurverGinzburg2004.jo_intendedContent_property_only : Discourse.Gameboard.reprisedContent joArrived joSub Discourse.Gameboard.RFReading.intendedContent = [Discourse.Gameboard.QueryType.property "jo"]

For 'Jo' (referential), the intended-content reprise queries a property over the sub-utterance's content — not an individual witness. The q-params channel is empty, so the property fallback applies.