Ginzburg and Cooper (2004): Clarification, Ellipsis, and the Nature of Contextual Updates in Dialogue #
This file formalizes the account of clarification ellipsis of [GC04], on which a
sign carries the contextual parameters its sub-utterances introduce
(LocutionaryProposition.parameters, LocutionaryProposition.constituents), grounding an
utterance is finding an assignment for all of them (Grounds, grounds_iff), and an addressee
who cannot updates the context instead by a coercion operation on the sign: parameter focussing
raises the question ?i.p, the content with the problematic parameter abstracted
(parameterFocussing), parameter identification the question what the speaker meant by the
sub-utterance (parameterIdentification), both making that sub-utterance salient
(focusEstablishing_parameterFocussing), and contextual existential generalization quantifies the
parameter away so that the weaker content can be grounded (existentialGeneralization,
grounds_existentialGeneralization). Since the operations read the constituents of the sign,
utterances with the same content have different clarification potentials
(potential_ne_of_constituents): the Hybrid Content Hypothesis, against the purely semantic
updates of dynamic semantics.
The utterance-processing protocol integrates a pending utterance whose parameters the
participant's assignment resolves and otherwise clarifies it (IS.ground, IS.clarify); after
"Did Bo leave?" the speaker's and the addressee's information states differ in MAX-QUD and
SAL-UTT (Ex32.differ), and the speaker comprehends the addressee's fragment by applying the
coercion to her own latest move (IS.backtrack, backtrack_eq_clarify). A fragment resolves
against the clarification context when it matches the salient sub-utterance in category
(DeclFrag); the clausal reading identifies its index with the parameter and so presupposes that
the participants share the sub-utterance's content, the constituent reading does not
(rows_clausal, rows_constituent), and a fragment of the wrong category has neither
(rows_parallelism).
Implementation notes #
- Signs are the substrate's
LocutionaryProposition, whose constituents' denotations name the parameter each contributes; contents are opaque, so existential generalization takes the binder as an argument, and parameter labels and contents are written as the paper's strings. A contextual parameter is its label: the restrictions of (28) are not represented, grounding asks only for a value, and the parameters an assignment leaves unresolved are those contextual instantiation of its labels leaves. - A coercion operation takes the problematic sub-utterance itself, whose denotation is the
parameter; the clarification context it yields is the substrate's
InformationStructure, with MAX-QUD as its question and SAL-UTT, a set of at most one sign, as its focus-establishing constituents. - The information state keeps the components that (82) displays: LATEST-MOVE as a sign with its assignment, PENDING, MAX-QUD and SAL-UTT; the FACTS update (81) and the grounding conditions (80) are not modelled.
- The constituent reading is licensed by categorial parallelism alone, the reformulation without utterance anaphora of footnote 55, so that the non-identical fragments of (8) get it; the categories of (10) are distinguished by the case or verb form the contrasts turn on.
References #
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- GinzburgCooper2004.instDecidableEqCategory x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- GinzburgCooper2004.instReprCategory = { reprPrec := GinzburgCooper2004.instReprCategory.repr }
The grammatical domain of the examples has orthographic forms and categories, with parameter labels and sub-utterance denotations written as the paper's strings.
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Contextual parameters and grounding #
A contextual assignment gives values to parameter labels.
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- GinzburgCooper2004.Assignment V = List (String × V)
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- GinzburgCooper2004.instDecidableResolves f i = { decide := decide (List.elem i (List.map Prod.fst f) = true), reflects_decide := ⋯ }
f grounds σ when it resolves every contextual parameter of the sign.
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- GinzburgCooper2004.Grounds f σ = ∀ i ∈ σ.parameters, f.Resolves i
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The parameters of σ that f leaves unresolved, those that remain once contextual
instantiation witnesses every parameter f assigns.
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- GinzburgCooper2004.unresolved f σ = (σ.instantiate (List.map Prod.fst f).toFinset).parameters
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Sign coercion #
The issues a clarification context makes maximal: the content posed, ?i.p with the
problematic parameter abstracted from the content (focussing), and ?c.Mean(addr, u, c), what the
speaker meant by the sub-utterance u (identification).
- posed {Cont : Type} (p : Cont) : Issue Cont
- focus {Cont : Type} (i : String) (p : Cont) : Issue Cont
- meaning {Cont : Type} (u : Discourse.SubUtterance grammar) : Issue Cont
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- GinzburgCooper2004.instDecidableEqIssue.decEq (GinzburgCooper2004.Issue.posed a) (GinzburgCooper2004.Issue.posed b) = if h : a = b then h ▸ isTrue ⋯ else isFalse ⋯
- GinzburgCooper2004.instDecidableEqIssue.decEq (GinzburgCooper2004.Issue.posed p) (GinzburgCooper2004.Issue.focus i p_1) = isFalse ⋯
- GinzburgCooper2004.instDecidableEqIssue.decEq (GinzburgCooper2004.Issue.posed p) (GinzburgCooper2004.Issue.meaning u) = isFalse ⋯
- GinzburgCooper2004.instDecidableEqIssue.decEq (GinzburgCooper2004.Issue.focus i p) (GinzburgCooper2004.Issue.posed p_1) = isFalse ⋯
- GinzburgCooper2004.instDecidableEqIssue.decEq (GinzburgCooper2004.Issue.focus i p) (GinzburgCooper2004.Issue.meaning u) = isFalse ⋯
- GinzburgCooper2004.instDecidableEqIssue.decEq (GinzburgCooper2004.Issue.meaning u) (GinzburgCooper2004.Issue.posed p) = isFalse ⋯
- GinzburgCooper2004.instDecidableEqIssue.decEq (GinzburgCooper2004.Issue.meaning u) (GinzburgCooper2004.Issue.focus i p) = isFalse ⋯
- GinzburgCooper2004.instDecidableEqIssue.decEq (GinzburgCooper2004.Issue.meaning a) (GinzburgCooper2004.Issue.meaning b) = if h : a = b then h ▸ isTrue ⋯ else isFalse ⋯
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A clarification context is the partial specification a coercion operation yields, the maximal question under discussion with the salient sub-utterance as its focus-establishing constituent.
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Parameter focussing makes u salient and MAX-QUD the content with its parameter abstracted,
?i.p, when u is a constituent of σ contributing one of its contextual parameters.
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Parameter identification makes u salient and MAX-QUD the question what the speaker meant by
it.
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The two operations differ only in MAX-QUD: they make the same sub-utterance salient.
Contextual existential generalization instantiates the parameter i and makes the content
bind i p, the content with i existentially bound with widest scope.
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An assignment resolving every parameter but i grounds the generalized sign.
The clarification potential of a sign: the clarification contexts its coercion operations make available.
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The subjects of (19)–(20), "Jill" and "She", both contributing the parameter j.
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- GinzburgCooper2004.jill = { form := "Jill", category := GinzburgCooper2004.Category.np, denotation := "j" }
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The subjects of (19)–(20), "Jill" and "She", both contributing the parameter j.
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- GinzburgCooper2004.she = { form := "She", category := GinzburgCooper2004.Category.np, denotation := "j" }
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"form is the president" with content p, its subject contributing the parameter j.
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- GinzburgCooper2004.president form subject p = { form := form, category := GinzburgCooper2004.Category.s, content := p, parameters := {"j"}, constituents := {subject} }
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The Hybrid Content Hypothesis as the paper argues it from (19)–(20): "Jill is the president" and "She is the president", with the same content and parameters, differ in clarification potential, because the potential reads the sub-utterances.
Integrating utterances in information states #
The components of a participant's information state that utterance processing reads and writes: LATEST-MOVE as the sign with its assignment, the utterances PENDING, and the clarification context MAX-QUD and SAL-UTT, a set of at most one sign (p. 327).
- latestMove : Option (Discourse.LocutionaryProposition grammar Cont × Assignment V)
- pending : List (Discourse.LocutionaryProposition grammar Cont)
- maxQud : Option (Issue Cont)
- salUtt : Finset (Discourse.SubUtterance grammar)
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Protocol (84a): the maximal pending utterance, once f grounds it, becomes LATEST-MOVE and
its content the issue posed.
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A coercion operation is a partial map from signs and their sub-utterances to clarification contexts.
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Protocol (84c): the maximal pending utterance stays pending, and MAX-QUD and SAL-UTT take the
values the coercion specifies for the sub-utterance u.
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Protocol (84b): the coercion applied to the sign of LATEST-MOVE, by which the speaker of an utterance comprehends a clarification of it.
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A coercion reads only the sign, so the speaker backtracking over her latest move and the addressee clarifying the same sign, pending for him, reach the same clarification context.
The running example, "Did Bo leave?" (32) #
The sub-utterances of (32), each with the parameter or relation it contributes.
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- GinzburgCooper2004.Ex32.did = { form := "Did", category := GinzburgCooper2004.Category.vFin, denotation := "ask" }
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- GinzburgCooper2004.Ex32.bo = { form := "Bo", category := GinzburgCooper2004.Category.np, denotation := "b" }
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- GinzburgCooper2004.Ex32.leave = { form := "leave", category := GinzburgCooper2004.Category.vBse, denotation := "leave" }
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- GinzburgCooper2004.Ex32.clause = { form := "Did Bo leave", category := GinzburgCooper2004.Category.s, denotation := "ask(i,j,?.leave(b,t))" }
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A's utterance: the root clause's parameters are the referent of "Bo", the time, the speaker, the addressee and the utterance time (28), (32).
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A's assignment (82b).
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- GinzburgCooper2004.Ex32.fA = [("b", "B"), ("t", "T0"), ("i", "A"), ("j", "B"), ("k", "T1"), ("s", "S0")]
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B's assignment (82c), with no value for the referent of "Bo".
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- GinzburgCooper2004.Ex32.fB = [("t", "T0"), ("i", "A"), ("j", "B"), ("k", "T1"), ("s", "S0")]
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Focussing on "Bo" makes it salient and asks who, named Bo, A is asking about (54).
Identification asks whom A meant by "Bo" (60).
With b generalized away, B's assignment grounds the weaker content (78).
The state after A's utterance, pending for both participants.
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- GinzburgCooper2004.Ex32.initial = { pending := [GinzburgCooper2004.Ex32.σ] }
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B clarifies by parameter focussing (82c).
The same utterance leaves the two participants with distinct MAX-QUD and SAL-UTT.
Backtracking with the same coercion, A reaches B's clarification context and can read "Bo?" as a clarification of her utterance (83).
Clarification ellipsis and its readings #
By decl-frag-cl (47), the fragment resolves against the clarification context when it matches the salient sub-utterance in category.
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- GinzburgCooper2004.DeclFrag c frag = ∃ u ∈ c.focusEstablishing, frag.category = u.category
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Whether the participants share (a belief about) the content of the sub-utterance.
- distinct : Access
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- GinzburgCooper2004.instDecidableEqAccess x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- GinzburgCooper2004.instReprAccess = { reprPrec := GinzburgCooper2004.instReprAccess.repr }
On the clausal reading the fragment resolves against a focussing context to the polar question whether the speaker is asking about this value of the parameter (58), identifying the fragment's index with the sub-utterance's, which presupposes shared content.
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On the constituent reading the fragment resolves against an identification context to the question what the speaker meant (68), presupposing nothing about the value.
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- GinzburgCooper2004.Constituent σ u frag = match GinzburgCooper2004.parameterIdentification σ u with | some c => GinzburgCooper2004.DeclFrag c frag | none => False
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A dialogue of §1.2: the sub-utterance clarified and the fragment, whether the participants share the sub-utterance's content, the readings the paper judges available, and the acceptability of the ellipsis.
- antecedent : Discourse.SubUtterance grammar
- fragment : Discourse.SubUtterance grammar
- access : Access
- clausal : Option Judgment
- constituent : Option Judgment
- judgment : Judgment
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The category labels of the data file.
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The sign of the row's first turn, as far as the clarification reads it, has the antecedent as
its constituent contributing the parameter x.
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- r.sign = { form := "", category := GinzburgCooper2004.Category.s, content := (), parameters := {"x"}, constituents := {r.antecedent} }
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The nineteen dialogues of (4), (6), (8)–(13).
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The clausal reading is judged available exactly when the fragment resolves against the focussing context with shared content.
The constituent reading is judged available exactly when the fragment resolves against the identification context.
Categorial parallelism (10): the ellipsis is acceptable exactly when some reading resolves it.