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Linglib.Phenomena.Reference.Studies.Ariel2001

@cite{ariel-2001} #

@cite{gundel-hedberg-zacharski-1993} @cite{cardinaletti-starke-1999}

Accessibility Theory: An Overview. In Sanders, Schilperoord & Spooren (eds.), Text Representation: Linguistic and Psycholinguistic Aspects, 29–87. John Benjamins.

Core Theory #

Referential form choice is governed by the degree of accessibility of the mental representation the speaker intends the addressee to retrieve. More accessible representations license more reduced referring expressions. Accessibility is gradient (not categorical) and is assessed via a composite of multiple factors.

The Accessibility Marking Scale #

The 18-level AccessibilityLevel type (defined in Core/Discourse/ReferentialForm.lean) encodes Ariel's ordering. This study file adds the three form-function criteria (informativity, rigidity, attenuation), the multi-factor accessibility assessment, and comparisons with competing theories.

Form-Function Criteria #

The ordering is motivated by three partially overlapping criteria, all anti-correlated with accessibility degree:

Informativity: amount of lexical content (more → lower accessibility)
Rigidity: ability to uniquely pick out a referent from form alone (proper names are rigid designators; descriptions are context-dependent)
Attenuation: phonological reduction (more reduced → higher accessibility)

Non-Equivalence with `DefinitenessLevel` #

The 5-level DefinitenessLevel scale (used for DOM/DSM in Core.Prominence) is a many-to-one coarsening of the 18-level scale, but the coarsening is not monotone: proper names are less accessible than definite descriptions on Ariel's scale (names are more informative, lower accessibility), but more prominent on Aissen's scale (names outrank definites for DOM).

Competing Theories #

Ariel argues accessibility theory subsumes @cite{gundel-hedberg-zacharski-1993}'s Givenness Hierarchy (a 6-level coarsening with weaker predictions) and is more comprehensive than Centering Theory (which handles only the pronoun/full-NP distinction, not the full range of referring expressions).

def Core.Discourse.ReferentialForm.AccessibilityLevel.informativity :

AccessibilityLevel → Nat

Informativity: approximate lexical content, encoded as an ordinal ranking (0–4). Anti-correlated with accessibility (more informative → lower rank). Values are illustrative, encoding the relative ordering described in @cite{ariel-2001} (p. 32), not exact content-word counts.

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def Core.Discourse.ReferentialForm.AccessibilityLevel.rigidity :

AccessibilityLevel → Nat

Rigidity: the ability to uniquely pick out a referent from form alone, independent of context. Anti-correlated with accessibility (more rigid → lower accessibility).

Proper names are rigid designators (Kripke): they pick out the same individual regardless of context. Definite descriptions are descriptive but context-dependent. Pronouns and zeros carry only person/number/gender features and are maximally non-rigid.

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def Core.Discourse.ReferentialForm.AccessibilityLevel.attenuation :

AccessibilityLevel → Nat

Attenuation: degree of phonological reduction. Positively correlated with accessibility. 0 = full, 5 = zero. Cliticized pronouns are shortened free pronouns (@cite{ariel-2001} note 6); verbal agreement inflections are bound morphemes, more reduced still; zero has no phonological material.

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def Core.Discourse.ReferentialForm.AccessibilityLevel.all :

List AccessibilityLevel

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theorem Phenomena.Reference.Studies.Ariel2001.zero_least_informative :

Core.Discourse.ReferentialForm.AccessibilityLevel.zero.informativity = 0 ∧ Core.Discourse.ReferentialForm.AccessibilityLevel.verbalAgreement.informativity = 0 ∧ Core.Discourse.ReferentialForm.AccessibilityLevel.cliticizedPron.informativity = 0

The highest-accessibility forms have the lowest informativity.

theorem Phenomena.Reference.Studies.Ariel2001.zero_most_attenuated :

Core.Discourse.ReferentialForm.AccessibilityLevel.zero.attenuation = 5

The highest-accessibility forms have the highest attenuation.

The three form-function criteria all correlate with accessibility in the predicted direction at the extremes of the scale:

Least accessible (fullNameMod): max informativity, max rigidity, min attenuation
Most accessible (zero): min informativity, min rigidity, max attenuation

theorem Phenomena.Reference.Studies.Ariel2001.names_rigid_pronouns_not :

Core.Discourse.ReferentialForm.AccessibilityLevel.fullName.rigidity > Core.Discourse.ReferentialForm.AccessibilityLevel.unstressedPron.rigidity ∧ Core.Discourse.ReferentialForm.AccessibilityLevel.fullName.rank < Core.Discourse.ReferentialForm.AccessibilityLevel.unstressedPron.rank

Names are rigid but low-accessibility; pronouns are non-rigid but high-accessibility. This is the rigidity–accessibility anti-correlation.

structure Phenomena.Reference.Studies.Ariel2001.AccessibilityAssessment :

Factors contributing to degree of accessibility of a discourse referent. Accessibility is a composite of all four; no single factor suffices.

distance : Nat
Clauses since last mention (0 = same clause). Lower → higher accessibility.
topicality : Fin 3
Discourse salience. 0=non-topic, 1=local topic, 2=global topic.
competition : Nat
Number of competing potential antecedents. Fewer → higher accessibility.
unity : Fin 3
Syntactic/semantic cohesion. 0=loose (coordination), 1=moderate (subordination), 2=tight (complement).

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instance Phenomena.Reference.Studies.Ariel2001.instReprAccessibilityAssessment :

Repr AccessibilityAssessment

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Phenomena.Reference.Studies.Ariel2001.instReprAccessibilityAssessment = { reprPrec := Phenomena.Reference.Studies.Ariel2001.instReprAccessibilityAssessment.repr }

def Phenomena.Reference.Studies.Ariel2001.instReprAccessibilityAssessment.repr :

AccessibilityAssessment → Nat → Std.Format

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def Phenomena.Reference.Studies.Ariel2001.AccessibilityAssessment.score (a : AccessibilityAssessment) :

Composite accessibility score (simplified additive model). Higher score → higher accessibility → more reduced form predicted.

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a.score = ↑a.topicality + ↑a.unity + (5 - min a.distance 5) + (3 - min a.competition 3)

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def Phenomena.Reference.Studies.Ariel2001.maximallyAccessible :

AccessibilityAssessment

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Phenomena.Reference.Studies.Ariel2001.maximallyAccessible = { distance := 0, topicality := 2, competition := 0, unity := 2 }

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def Phenomena.Reference.Studies.Ariel2001.minimallyAccessible :

AccessibilityAssessment

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Phenomena.Reference.Studies.Ariel2001.minimallyAccessible = { distance := 5, topicality := 0, competition := 3, unity := 0 }

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theorem Phenomena.Reference.Studies.Ariel2001.maximal_gt_minimal :

maximallyAccessible.score > minimallyAccessible.score

theorem Phenomena.Reference.Studies.Ariel2001.coarsening_not_monotone :

Core.Discourse.ReferentialForm.AccessibilityLevel.fullName.rank < Core.Discourse.ReferentialForm.AccessibilityLevel.longDefDescription.rank ∧ Core.Discourse.ReferentialForm.AccessibilityLevel.fullName.toDefLevel.rank > Core.Discourse.ReferentialForm.AccessibilityLevel.longDefDescription.toDefLevel.rank

The coarsening is NOT monotone: "full name" (accessibility rank 1) maps to properName (definiteness rank 3), but "long definite description" (accessibility rank 2) maps to definite (definiteness rank 2). Higher accessibility maps to LOWER definiteness rank here.

This proves that Ariel's accessibility scale and Aissen's definiteness scale capture genuinely different orderings: names are less accessible (more informative) but more prominent (higher on the DOM hierarchy).

def Phenomena.Reference.Studies.Ariel2001.strengthToAccessibility :

Anaphora.Typology.PronounStrength → Core.Discourse.ReferentialForm.AccessibilityLevel

@cite{cardinaletti-starke-1999}'s three-way pronoun strength maps to positions on the accessibility scale. strong → stressedPron, weak → unstressedPron, clitic → cliticizedPron.

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theorem Phenomena.Reference.Studies.Ariel2001.strength_matches_accessibility :

(strengthToAccessibility Anaphora.Typology.PronounStrength.clitic).rank > (strengthToAccessibility Anaphora.Typology.PronounStrength.weak).rank ∧ (strengthToAccessibility Anaphora.Typology.PronounStrength.weak).rank > (strengthToAccessibility Anaphora.Typology.PronounStrength.strong).rank

Pronoun strength ordering matches accessibility ordering: clitic > weak > strong in accessibility.

theorem Phenomena.Reference.Studies.Ariel2001.strength_coarsening_agrees :

(strengthToAccessibility Anaphora.Typology.PronounStrength.strong).toDefLevel = Core.Prominence.DefinitenessLevel.personalPronoun ∧ (strengthToAccessibility Anaphora.Typology.PronounStrength.weak).toDefLevel = Core.Prominence.DefinitenessLevel.personalPronoun ∧ (strengthToAccessibility Anaphora.Typology.PronounStrength.clitic).toDefLevel = Core.Prominence.DefinitenessLevel.personalPronoun

All three pronoun strengths coarsen to the same definiteness level.

inductive Phenomena.Reference.Studies.Ariel2001.GivennessStatus :

Gundel, Hedberg & Zacharski (1993): six cognitive statuses organized as an implicational hierarchy. Each status implies all lower ones.

in focus > activated > familiar > uniquely identifiable > referential > type identifiable

inFocus : GivennessStatus
activated : GivennessStatus
familiar : GivennessStatus
uniquelyIdentifiable : GivennessStatus
referential : GivennessStatus
typeIdentifiable : GivennessStatus

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instance Phenomena.Reference.Studies.Ariel2001.instDecidableEqGivennessStatus :

DecidableEq GivennessStatus

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Phenomena.Reference.Studies.Ariel2001.instDecidableEqGivennessStatus x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Reference.Studies.Ariel2001.instBEqGivennessStatus :

BEq GivennessStatus

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Phenomena.Reference.Studies.Ariel2001.instBEqGivennessStatus = { beq := Phenomena.Reference.Studies.Ariel2001.instBEqGivennessStatus.beq }

def Phenomena.Reference.Studies.Ariel2001.instBEqGivennessStatus.beq :

GivennessStatus → GivennessStatus → Bool

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Phenomena.Reference.Studies.Ariel2001.instBEqGivennessStatus.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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instance Phenomena.Reference.Studies.Ariel2001.instReprGivennessStatus :

Repr GivennessStatus

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Phenomena.Reference.Studies.Ariel2001.instReprGivennessStatus = { reprPrec := Phenomena.Reference.Studies.Ariel2001.instReprGivennessStatus.repr }

def Phenomena.Reference.Studies.Ariel2001.instReprGivennessStatus.repr :

GivennessStatus → Nat → Std.Format

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def Phenomena.Reference.Studies.Ariel2001.GivennessStatus.toAccessibility :

GivennessStatus → Core.Discourse.ReferentialForm.AccessibilityLevel

Prototypical accessibility level for each givenness status.

Caveat: Gundel et al.'s lower statuses (referential = "indefinite this N", typeIdentifiable = "a N") correspond to indefinite expressions, which do not appear on Ariel's accessibility marking scale (which covers Given/definite referential forms). The mapping for these two is by approximate accessibility degree, not by form identity. Ariel herself notes (p. 63) that the Givenness Hierarchy's coverage is "suspiciously compatible with the distribution of just those referring expressions linguists have tended to focus on."

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theorem Phenomena.Reference.Studies.Ariel2001.givenness_coarsening_monotone :

have all := [GivennessStatus.inFocus , GivennessStatus.activated , GivennessStatus.familiar , GivennessStatus.uniquelyIdentifiable , GivennessStatus.referential , GivennessStatus.typeIdentifiable ]; (all.all fun (a : GivennessStatus) => all.all fun (b : GivennessStatus) => if a.rank > b.rank then decide (a.toAccessibility.rank ≥ b.toAccessibility.rank) else true) = true

The Givenness→Accessibility mapping IS monotone: higher givenness status maps to higher or equal accessibility rank. The Givenness Hierarchy is a well-behaved (but lossy) coarsening of Ariel's scale.

theorem Phenomena.Reference.Studies.Ariel2001.givenness_collapses_pronominal_distinctions :

Core.Discourse.ReferentialForm.AccessibilityLevel.unstressedPron.toDefLevel = Core.Prominence.DefinitenessLevel.personalPronoun ∧ Core.Discourse.ReferentialForm.AccessibilityLevel.cliticizedPron.toDefLevel = Core.Prominence.DefinitenessLevel.personalPronoun ∧ Core.Discourse.ReferentialForm.AccessibilityLevel.verbalAgreement.toDefLevel = Core.Prominence.DefinitenessLevel.personalPronoun ∧ Core.Discourse.ReferentialForm.AccessibilityLevel.zero.toDefLevel = Core.Prominence.DefinitenessLevel.personalPronoun ∧ Core.Discourse.ReferentialForm.AccessibilityLevel.zero.rank > Core.Discourse.ReferentialForm.AccessibilityLevel.verbalAgreement.rank ∧ Core.Discourse.ReferentialForm.AccessibilityLevel.verbalAgreement.rank > Core.Discourse.ReferentialForm.AccessibilityLevel.cliticizedPron.rank ∧ Core.Discourse.ReferentialForm.AccessibilityLevel.cliticizedPron.rank > Core.Discourse.ReferentialForm.AccessibilityLevel.unstressedPron.rank

Four accessibility levels that the Givenness Hierarchy collapses into "in focus" have genuinely different accessibility ranks and different discourse distributions (p. 64). The 6-level hierarchy asks: "How can we distinguish between zeroes and pronouns in a language which uses both as very high accessibility markers... Both must be classified as 'in focus' markers, but they each have a distinct distributional pattern."

theorem Phenomena.Reference.Studies.Ariel2001.proximate_more_accessible_than_distal :

Core.Discourse.ReferentialForm.AccessibilityLevel.proxDem.rank > Core.Discourse.ReferentialForm.AccessibilityLevel.distalDem.rank ∧ Core.Discourse.ReferentialForm.AccessibilityLevel.proxDemNP.rank > Core.Discourse.ReferentialForm.AccessibilityLevel.distalDemNP.rank

Proximate demonstratives code higher accessibility than distal ones. Both are "activated" in the Givenness Hierarchy — the 6-level system cannot capture this contrast.

theorem Phenomena.Reference.Studies.Ariel2001.predictedForm_uses_accessibility :

Core.Discourse.ReferentialForm.NextMentionBias.high.predictedForm = Core.Discourse.ReferentialForm.AccessibilityLevel.unstressedPron ∧ Core.Discourse.ReferentialForm.NextMentionBias.low.predictedForm = Core.Discourse.ReferentialForm.AccessibilityLevel.fullName

The NextMentionBias prediction directly uses accessibility levels: high bias → unstressed pronoun (high accessibility), low bias → full name (low accessibility). This is the core of @cite{ariel-2001}'s theory: more accessible → more reduced form.

The predicted forms are the RIGHT forms, not a coarsened approximation through DefinitenessLevel.