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Studies.Ariel2001

Ariel 2001: accessibility theory #

Referring expressions are accessibility markers: each codes a degree of mental accessibility of the representation the addressee is to retrieve, and the eighteen classes of the Accessibility Marking Scale run from full name with modifier down to zero. The scale is motivated by three partially overlapping criteria — informativity, rigidity, and attenuation — each anti-correlated with the accessibility a form codes. The accessibility of a representation is a composite of the antecedent's salience (discourse topics, speaker and addressee, frame-induced entities), competition among antecedents, distance, and the unity between antecedent and anaphor; no single factor decides, as when a topical but distant antecedent takes the higher marker over a recent non-topical one. Against the rival theories, the Givenness Hierarchy maps many forms of distinct accessibility to one status and one form to several, and Centering's pronoun rule is silent on lexical anaphors, so it does not predict the repeated-name penalty.

Main definitions #

References #

Form-function criteria (§1.1) #

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theorem Ariel2001.informativity_modifier (a b : Discourse.AccessibilityLevel) :
a.head = b.head → a.deixis = b.deixis → a.modified → ¬b.modified → a < b

By informativity, a modifier lowers the accessibility a form codes.

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theorem Ariel2001.informativity_lexical (a b : Discourse.AccessibilityLevel) :
a.head = b.head → a.deixis = b.deixis → ¬a.modified → ¬b.modified → a.lexical → ¬b.lexical → a < b

By informativity, a demonstrative with a noun codes lower accessibility than a bare one.

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theorem Ariel2001.informativity_partial_name (a b : Discourse.AccessibilityLevel) :
a.head = Discourse.AccessibilityLevel.Head.name → b.head = Discourse.AccessibilityLevel.Head.name → ¬a.modified → ¬b.modified → a.full → ¬b.full → a < b

By informativity, a full name codes lower accessibility than a partial one.

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theorem Ariel2001.rigidity_full_name (a b : Discourse.AccessibilityLevel) :
a.head = Discourse.AccessibilityLevel.Head.name → a.full → b.head = Discourse.AccessibilityLevel.Head.description → a.modified = b.modified → a < b

By rigidity, a full name codes lower accessibility than the description of the same length.

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theorem Ariel2001.rigidity_not_sufficient :
Discourse.AccessibilityLevel.shortDefDescription < Discourse.AccessibilityLevel.lastName

The criteria overlap only partially: a partial name is rigid, yet codes higher accessibility than a short description.

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theorem Ariel2001.attenuation_stress (a b : Discourse.AccessibilityLevel) :
a.head = Discourse.AccessibilityLevel.Head.pronoun → b.head = Discourse.AccessibilityLevel.Head.pronoun → a.stressed → ¬b.stressed → a < b

By attenuation, a stressed pronoun codes lower accessibility than an unstressed one.

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theorem Ariel2001.attenuation_reduction (a b : Discourse.AccessibilityLevel) :
a.head = Discourse.AccessibilityLevel.Head.pronoun ∧ b.head = Discourse.AccessibilityLevel.Head.pronoun ∧ ¬a.stressed ∧ ¬a.bound ∧ b.bound ∨ a.head = Discourse.AccessibilityLevel.Head.pronoun ∧ b.head = Discourse.AccessibilityLevel.Head.inflection ∨ a.head = Discourse.AccessibilityLevel.Head.inflection ∧ b.head = Discourse.AccessibilityLevel.Head.zero → a < b

By attenuation, a free pronoun codes lower accessibility than a cliticized one, a pronoun than verbal agreement, and agreement than zero.

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theorem Ariel2001.deixis_proximate (a b : Discourse.AccessibilityLevel) :
a.head = Discourse.AccessibilityLevel.Head.demonstrative → b.head = Discourse.AccessibilityLevel.Head.demonstrative → a.modified = b.modified → a.lexical = b.lexical → a.deixis = some Person.first.participantSetsᶜ → b.deixis = some Person.first.participantSets → a < b

The proximate demonstrative codes higher accessibility than the distal one of the same shape (§5.1 records Kirsner's Dutch data against this).

Accessibility as a complex concept (§1.2) #

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inductive Ariel2001.Topicality :
Type

The salience of an antecedent by discourse role.

Instances For
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    @[instance_reducible]
    instance Ariel2001.instDecidableEqTopicality :
    DecidableEq Topicality
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    def Ariel2001.instReprTopicality.repr :
    Topicality → ℕ → Std.Format
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    • One or more equations did not get rendered due to their size.
    Instances For
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      @[instance_reducible]
      instance Ariel2001.instReprTopicality :
      Repr Topicality
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      def Ariel2001.Topicality.rank :
      Topicality → ℕ

      Topicality in increasing order.

      Equations
      Instances For
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        structure Ariel2001.Factors :
        Type

        A degree of accessibility is assessed from distance since the last mention, competing antecedents, topicality, and the unity of antecedent and anaphor.

        • distance : ℕ
        • competitors : ℕ
        • topicality : Topicality
        • tight : Bool
        Instances For
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          @[instance_reducible]
          instance Ariel2001.instDecidableEqFactors :
          DecidableEq Factors
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          def Ariel2001.instDecidableEqFactors.decEq (x✝ x✝¹ : Factors) :
          Decidable (x✝ = x✝¹)
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          • One or more equations did not get rendered due to their size.
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            def Ariel2001.instReprFactors.repr :
            Factors → ℕ → Std.Format
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            • One or more equations did not get rendered due to their size.
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              @[instance_reducible]
              instance Ariel2001.instReprFactors :
              Repr Factors
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              def Ariel2001.Factors.Dominates (a b : Factors) :
              Prop

              a is at least as accessible as b on every factor.

              Equations
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                @[instance_reducible]
                instance Ariel2001.instDecidableDominates (a b : Factors) :
                Decidable (a.Dominates b)
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                def Ariel2001.maya :
                Factors

                In Maya kissed Rachel. And then she/SHE … the first-mentioned Maya is topical but more distant, Rachel more recent but not topical.

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                Instances For
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                  def Ariel2001.rachel :
                  Factors

                  Rachel's factors in the same example.

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                    theorem Ariel2001.maya_rachel_incomparable :
                    ¬maya.Dominates rachel ∧ ¬rachel.Dominates maya

                    Neither antecedent dominates the other: the factors pull apart.

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                    def Ariel2001.ofLabel :
                    String → Option Discourse.AccessibilityLevel

                    The scale label of a marker feature.

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                    Instances For
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                      def Ariel2001.marker (r : Datum) (key : String) :
                      Option Discourse.AccessibilityLevel

                      The marker a row records under a feature.

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                        def Ariel2001.markers (r : Datum) :
                        List Discourse.AccessibilityLevel

                        All the markers a row lists, in order.

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                        Instances For
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                          theorem Ariel2001.rows_topicality_over_distance (r : Datum) :
                          r ∈ Examples.all → ∀ m ∈ (marker r "maya").toList, ∀ c ∈ (marker r "rachel").toList, c < m

                          Topicality outranks distance: the topical, more distant Maya takes the higher marker.

                          source
                          theorem Ariel2001.rows_perspective (r : Datum) :
                          r ∈ Examples.all → ∀ v ∈ (marker r "victim").toList, ∀ p ∈ (marker r "rapists").toList, (r.feature? "perspective" = some "victim" → p < v) ∧ (r.feature? "perspective" = some "rapists" → v < p)

                          Comparing (3) with (4), the entity whose point of view a newspaper takes is coded by the higher marker: the victim by zero and the rapist by a name in Haaretz, the rapists by zero and the victim by a demonstrative in Maariv.

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                          theorem Ariel2001.rows_headline (a : Datum) :
                          a ∈ Examples.all → ∀ b ∈ Examples.all, a.source.paperLabel = "(8a)" → b.source.paperLabel = "(8b)" → ∀ p ∈ (markers a).zip (markers b), p.2 < p.1

                          (8): every referring expression of the article's opening sentence codes lower accessibility than its counterpart in the headline — initial retrievals, but of entities the headline has just made accessible.

                          Competing theories (§4) #

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                          def Ariel2001.givenness :
                          Discourse.AccessibilityLevel → Finset Discourse.GivennessStatus

                          The Givenness Hierarchy statuses of the scale's forms, as the paper reports them for English: the pronominal forms are all in focus, that, this, stressed IT, and this N all activated, and a full name uniquely identifiable or familiar, a partial name familiar or activated.

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                            theorem Ariel2001.activated_many_forms :
                            (∀ l ∈ [Discourse.AccessibilityLevel.distalDem, Discourse.AccessibilityLevel.proxDem, Discourse.AccessibilityLevel.stressedPron, Discourse.AccessibilityLevel.proxDemNP], givenness l = {Discourse.GivennessStatus.activated}) ∧ (List.map Discourse.AccessibilityLevel.rank [Discourse.AccessibilityLevel.distalDem, Discourse.AccessibilityLevel.proxDem, Discourse.AccessibilityLevel.stressedPron, Discourse.AccessibilityLevel.proxDemNP]).Nodup

                            Many forms, one status: four forms of distinct accessibility are all activated.

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                            theorem Ariel2001.full_name_two_statuses :
                            Discourse.GivennessStatus.uniquelyIdentifiable ∈ givenness Discourse.AccessibilityLevel.fullName ∧ Discourse.GivennessStatus.familiar ∈ givenness Discourse.AccessibilityLevel.fullName

                            One form, many statuses: a full name is uniquely identifiable or familiar.

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                            theorem Ariel2001.in_focus_collapse :
                            (∀ l ∈ [Discourse.AccessibilityLevel.zero, Discourse.AccessibilityLevel.verbalAgreement, Discourse.AccessibilityLevel.cliticizedPron, Discourse.AccessibilityLevel.unstressedPron], givenness l = {Discourse.GivennessStatus.inFocus}) ∧ (List.map Discourse.AccessibilityLevel.rank [Discourse.AccessibilityLevel.zero, Discourse.AccessibilityLevel.verbalAgreement, Discourse.AccessibilityLevel.cliticizedPron, Discourse.AccessibilityLevel.unstressedPron]).Nodup

                            Zeroes, agreement, cliticized and full pronouns are all in focus, though each codes a different degree of accessibility and has its own distribution.

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                            theorem Ariel2001.pronominalization_vacuous {E : Type u_1} {R : Type u_2} [DecidableEq E] [LinearOrder R] (prev cur : Discourse.Centering.Utterance E R) (h : ∀ (e : E), ¬cur.Pronominalizes e) :
                            Discourse.Centering.PronominalizationConstraint prev cur

                            Centering's pronoun rule says nothing when no pronoun is used, so an entity coded by a repeated name violates nothing: the repeated-name penalty is not its prediction.

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                            theorem Ariel2001.rows_topic_over_subject (r : Datum) :
                            r ∈ Examples.all → ∀ t ∈ (marker r "topicMarker").toList, ∀ s ∈ (marker r "subjectMarker").toList, s < t

                            (12): the discourse topic is pronominal while the subject of two consecutive clauses is a description — the topic, not the local subject, takes the higher marker.