Ginzburg & Cooper (2004): Clarification, Ellipsis, and Contextual Updates

@cite{ginzburg-cooper-2004}

Formalization of the core running example from @cite{ginzburg-cooper-2004}:

A: "Did Bo leave?" B: "Bo?"

This study applies the KOS framework (DGB, IS, C-PARAMS, coercion operations) to derive both CE readings — clausal and constituent — from the same antecedent sign, and demonstrates the speaker/addressee IS asymmetry.

Key Claims Formalized

1. Proper names introduce C-PARAMS (referent binding) — ex. 28
2. The running example has 5 C-PARAMS — ex. 32
3. Parameter focussing yields clausal CE reading — ex. 53/54
4. Parameter identification yields constituent CE reading — ex. 59/60
5. Both coercions take the antecedent sign and target the same SAL-UTT
6. Existential generalization removes a parameter without clarification — ex. 77/78
7. Speaker resolves all params; addressee may not — ex. 82
8. Partial assignment triggers PENDING, not grounding
9. Updates require structured representations (Hybrid Content Hypothesis) — ex. 2/16

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.cpBo : Theories.Pragmatics.Dialogue.KOS.CParam

C-PARAM for "Bo": binds variable b to the referent named "Bo". @cite{ginzburg-cooper-2004} ex. 28.

Equations

• Phenomena.Ellipsis.Studies.GinzburgCooper2004.cpBo = { index := "b", restriction := "named(Bo)(b)" }

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.cpTime : Theories.Pragmatics.Dialogue.KOS.CParam

C-PARAM for temporal precedence.

Equations

• Phenomena.Ellipsis.Studies.GinzburgCooper2004.cpTime = { index := "t", restriction := "precedes(t,k)" }

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.cpSpkr : Theories.Pragmatics.Dialogue.KOS.CParam

C-PARAM for speaker.

Equations

• Phenomena.Ellipsis.Studies.GinzburgCooper2004.cpSpkr = { index := "i", restriction := "spkr(i)" }

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.cpAddr : Theories.Pragmatics.Dialogue.KOS.CParam

C-PARAM for addressee.

Equations

• Phenomena.Ellipsis.Studies.GinzburgCooper2004.cpAddr = { index := "j", restriction := "addr(j)" }

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.cpUttTime : Theories.Pragmatics.Dialogue.KOS.CParam

C-PARAM for utterance time.

Equations

• Phenomena.Ellipsis.Studies.GinzburgCooper2004.cpUttTime = { index := "k", restriction := "utt-time(k)" }

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.didBoLeaveCParams : Theories.Pragmatics.Dialogue.KOS.CParamSet

The full C-PARAMS set for "Did Bo leave?" — 5 parameters. @cite{ginzburg-cooper-2004} ex. 32.

Equations

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

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.suDid : Theories.Pragmatics.Dialogue.KOS.SubUtterance

Equations

• Phenomena.Ellipsis.Studies.GinzburgCooper2004.suDid = { phon := "Did", cat := "AUX", cont := "ask" }

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.suBo : Theories.Pragmatics.Dialogue.KOS.SubUtterance

Equations

• Phenomena.Ellipsis.Studies.GinzburgCooper2004.suBo = { phon := "Bo", cat := "NP", cont := "b" }

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.suLeave : Theories.Pragmatics.Dialogue.KOS.SubUtterance

Equations

• Phenomena.Ellipsis.Studies.GinzburgCooper2004.suLeave = { phon := "leave", cat := "V", cont := "leave-rel" }

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.suDidBoLeave : Theories.Pragmatics.Dialogue.KOS.SubUtterance

Equations

• Phenomena.Ellipsis.Studies.GinzburgCooper2004.suDidBoLeave = { phon := "Did Bo leave", cat := "S", cont := "ask(i,j,?.leave-rel(b,t))" }

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.didBoLeave : Theories.Pragmatics.Dialogue.KOS.UttSkeleton

Full utterance skeleton for "Did Bo leave?" with all 5 C-PARAMS. @cite{ginzburg-cooper-2004} ex. 32.

Equations

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

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.speakerAssignment : Theories.Pragmatics.Dialogue.KOS.CtxtAssignment

Speaker (A) resolves all parameters: she knows who Bo is, who she is, who the addressee is, and the temporal parameters. @cite{ginzburg-cooper-2004} ex. 82b.

Equations

• Phenomena.Ellipsis.Studies.GinzburgCooper2004.speakerAssignment = { bindings := [("b", "B"), ("t", "T0"), ("i", "A"), ("j", "B"), ("k", "T1")] }

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.addresseeAssignment : Theories.Pragmatics.Dialogue.KOS.CtxtAssignment

Addressee (B) resolves all parameters EXCEPT b (Bo's referent). B doesn't know who "Bo" refers to. @cite{ginzburg-cooper-2004} ex. 82c.

Equations

• Phenomena.Ellipsis.Studies.GinzburgCooper2004.addresseeAssignment = { bindings := [("t", "T0"), ("i", "A"), ("j", "B"), ("k", "T1")] }

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.speakerIS : Theories.Pragmatics.Dialogue.KOS.IS String String

A's IS after uttering "Did Bo leave?": fully grounded. Speaker resolves all C-PARAMS, so the utterance goes straight to FACTS.

Equations

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

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.addresseeIS : Theories.Pragmatics.Dialogue.KOS.IS String String

B's IS after hearing "Did Bo leave?": partial assignment → pending. Addressee cannot resolve b, so the utterance goes to PENDING.

Equations

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

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.focussingOnBo : Option Theories.Pragmatics.Dialogue.KOS.CoercionOutput

Parameter focussing on "Bo" (parameter b): clausal CE reading. @cite{ginzburg-cooper-2004} ex. 53–54. Output: SAL-UTT = "Bo" constituent, MAX-QUD = ?b.ask(i,j,?.leave-rel(b,t)) Paraphrase: "Are you asking if b left?"

Equations

• Phenomena.Ellipsis.Studies.GinzburgCooper2004.focussingOnBo = Theories.Pragmatics.Dialogue.KOS.parameterFocussing Phenomena.Ellipsis.Studies.GinzburgCooper2004.didBoLeave "b"

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.identificationOnBo : Option Theories.Pragmatics.Dialogue.KOS.CoercionOutput

Parameter identification on "Bo" (parameter b): constituent CE reading. @cite{ginzburg-cooper-2004} ex. 59–60. Output: SAL-UTT = "Bo" constituent, MAX-QUD = ?c.spkr-meaning-rel(addr,Bo,c) Paraphrase: "Who do you mean by Bo?"

Equations

• Phenomena.Ellipsis.Studies.GinzburgCooper2004.identificationOnBo = Theories.Pragmatics.Dialogue.KOS.parameterIdentification Phenomena.Ellipsis.Studies.GinzburgCooper2004.didBoLeave "b"

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.existGenOnBo : Theories.Pragmatics.Dialogue.KOS.UttSkeleton

Existential generalization on "Bo" (parameter b). @cite{ginzburg-cooper-2004} ex. 77–78. Removes b from C-PARAMS, weakens content to ∃b.ask(i,j,?.leave-rel(b,t)).

Equations

• Phenomena.Ellipsis.Studies.GinzburgCooper2004.existGenOnBo = Theories.Pragmatics.Dialogue.KOS.existentialGeneralization Phenomena.Ellipsis.Studies.GinzburgCooper2004.didBoLeave "b"

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.addresseeISAfterFocussing : Option (Theories.Pragmatics.Dialogue.KOS.IS String String)

B applies parameter focussing to set up clarification context.

Equations

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

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.addresseeISAfterIdentification : Option (Theories.Pragmatics.Dialogue.KOS.IS String String)

B applies parameter identification to set up clarification context.

Equations

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

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.five_cparams : List.length didBoLeave.cparams = 5

The running example has exactly 5 C-PARAMS.

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.four_constits : didBoLeave.constits.length = 4

The running example has 4 constituents (Did, Bo, leave, Did Bo leave).

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.speaker_resolves_all : speakerAssignment.resolvesAll didBoLeaveCParams = true

Speaker resolves all C-PARAMS.

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.addressee_partial : addresseeAssignment.resolvesAll didBoLeaveCParams = false

Addressee does NOT resolve all C-PARAMS (missing b).

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.addressee_unresolved_is_bo : List.map Theories.Pragmatics.Dialogue.KOS.CParam.index (addresseeAssignment.unresolved didBoLeaveCParams) = ["b"]

The unresolved parameter for B is exactly {b}.

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.speaker_grounds : speakerIS.dgb.facts = ["ask(i,j,?.leave-rel(b,t))"]

Speaker's utterance is grounded (added to FACTS).

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.addressee_no_facts : addresseeIS.dgb.facts = []

Addressee's utterance is NOT grounded (no new facts).

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.addressee_has_pending : addresseeIS.pending.length = 1

Addressee's utterance goes to PENDING.

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.focussing_available : focussingOnBo.isSome = true

Parameter focussing succeeds on "Bo".

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.identification_available : identificationOnBo.isSome = true

Parameter identification succeeds on "Bo".

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.coercions_same_salUtt : Option.map Theories.Pragmatics.Dialogue.KOS.CoercionOutput.salUtt focussingOnBo = Option.map Theories.Pragmatics.Dialogue.KOS.CoercionOutput.salUtt identificationOnBo

Both coercions target the same SAL-UTT (the "Bo" constituent).

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.salUtt_is_bo : Option.map (fun (x : Theories.Pragmatics.Dialogue.KOS.CoercionOutput) => x.salUtt.phon) focussingOnBo = some "Bo"

The SAL-UTT is "Bo".

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.different_ops : Option.map Theories.Pragmatics.Dialogue.KOS.CoercionOutput.op focussingOnBo ≠ Option.map Theories.Pragmatics.Dialogue.KOS.CoercionOutput.op identificationOnBo

Focussing and identification produce different operation types.

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.exist_gen_removes_bo : List.length existGenOnBo.cparams = 4

Existential generalization removes exactly one parameter.

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.exist_gen_keeps_others : List.map Theories.Pragmatics.Dialogue.KOS.CParam.index existGenOnBo.cparams = ["t", "i", "j", "k"]

The removed parameter is b.

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.exist_gen_weakens_content : existGenOnBo.cont = "∃b.ask(i,j,?.leave-rel(b,t))"

Existential generalization wraps content with ∃.

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.focussing_maxqud : Option.map (fun (x : Theories.Pragmatics.Dialogue.KOS.CoercionOutput) => x.maxQud) focussingOnBo = some "?b.ask(i,j,?.leave-rel(b,t))"

Focussing MAX-QUD is a question about the antecedent content.

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.identification_maxqud : Option.map (fun (x : Theories.Pragmatics.Dialogue.KOS.CoercionOutput) => x.maxQud) identificationOnBo = some "?c.spkr-meaning-rel(addr,Bo,c)"

Identification MAX-QUD is a speaker-meaning question.

def Phenomena.Ellipsis.Studies.GinzburgCooper2004.coercionToReading : Theories.Pragmatics.Dialogue.KOS.CoercionOp → ClarificationEllipsis.CEReading

The KOS theory's coercion operations correspond to the empirical CE readings: parameterFocussing ↔ clausal, parameterIdentification ↔ constituent. @cite{ginzburg-cooper-2004} §5.

Equations

• One or more equations did not get rendered due to their size.
• Phenomena.Ellipsis.Studies.GinzburgCooper2004.coercionToReading Theories.Pragmatics.Dialogue.KOS.CoercionOp.paramFocussing = Phenomena.Ellipsis.ClarificationEllipsis.CEReading.clausal
• Phenomena.Ellipsis.Studies.GinzburgCooper2004.coercionToReading Theories.Pragmatics.Dialogue.KOS.CoercionOp.paramIdentification = Phenomena.Ellipsis.ClarificationEllipsis.CEReading.constituent

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.readings_biject_coercions : coercionToReading Theories.Pragmatics.Dialogue.KOS.CoercionOp.paramFocussing ≠ coercionToReading Theories.Pragmatics.Dialogue.KOS.CoercionOp.paramIdentification

The CE data's two readings map to distinct coercion operations.

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.hybrid_content_evidence : didBoLeave.constitForParam "b" = some suBo ∧ didBoLeave.constitForParam "leave-rel" = some suLeave

Hybrid Content Hypothesis (@cite{ginzburg-cooper-2004} ex. 2/16): The content updated in dynamic semantics consists of structure expressing detailed relationships between the content and formal properties (syntax, phonology etc) of the various parts of an utterance.

Evidence: The same propositional content ("Bo left") yields different clarification potentials depending on phonological/syntactic structure. The utterance skeleton encodes this structure via CONSTITS and C-PARAMS.

theorem Phenomena.Ellipsis.Studies.GinzburgCooper2004.running_example_matches_ce_data : ClarificationEllipsis.ceProperName.readings = [ClarificationEllipsis.CEReading.clausal, ClarificationEllipsis.CEReading.constituent]

The CE proper name example matches our running example.