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Studies.WesterbeekKoolenMaes2015

Westerbeek, Koolen & Maes (2015): Stored Object Knowledge and the Production of Referring Expressions #

This file formalizes the computational claim of [WKM15]. In two production experiments, speakers referring to an object whose type alone distinguishes it from the distractors mention its color more often the less typical that color is for the object, and more so for objects whose shape is less diagnostic, which the paper attributes to a contrast with the color stored with the object's category. The paper argues that models of content determination without object knowledge cannot capture this: [DR95]'s Incremental Algorithm, which considers attributes in a fixed preference order and keeps one only when it rules out a remaining distractor, produces the bare head noun whenever the type distinguishes the referent, whatever the colors in the scene (flat_makeReferringExpression_type), so its output for a yellow and a red tomato is the same (makeReferringExpression_congr_type) and its color-mention rate cannot vary with typicality (decision_rule_not_ia).

Implementation notes #

The scenes are the flat domains of the Incremental Algorithm's user model, in which the user knows a property exactly when the scene has it. The paper's decision rule, that the probability of mentioning a property rises with its contrast to stored knowledge, is a strictly decreasing rate in the typicality score; the experiments' rates and regression coefficients are reported in the paper and not formalized.

References #

The Incremental Algorithm on a type-distinguished referent #

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theorem WesterbeekKoolenMaes2015.flat_makeReferringExpression_type {E : Type u_1} {A : Type u_2} {V : Type u_3} [DecidableEq E] [DecidableEq A] [DecidableEq V] (kb : DaleReiter1995.KB E A V) (t : A) (r : E) (C : Finset E) (rest : List A) {v : V} (hr : kb r t = some v) (hC : ∀ c ∈ C, ∃ (w : V), kb c t = some w ∧ w ≠ v) :
(DaleReiter1995.Domain.flat kb t).makeReferringExpression r C (t :: rest) = some {(t, v)}

When the referent's type rules out every distractor and type heads the preference order, the Incremental Algorithm returns the bare head noun, whatever the other attributes hold.

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theorem WesterbeekKoolenMaes2015.makeReferringExpression_congr_type {E : Type u_1} {A : Type u_2} {V : Type u_3} [DecidableEq E] [DecidableEq A] [DecidableEq V] (kb₁ kb₂ : DaleReiter1995.KB E A V) (t : A) (r : E) (C : Finset E) (rest : List A) (h : ∀ (x : E), kb₁ x t = kb₂ x t) {v : V} (hr : kb₁ r t = some v) (hC : ∀ c ∈ C, ∃ (w : V), kb₁ c t = some w ∧ w ≠ v) :
(DaleReiter1995.Domain.flat kb₁ t).makeReferringExpression r C (t :: rest) = (DaleReiter1995.Domain.flat kb₂ t).makeReferringExpression r C (t :: rest)

Two scenes with the same types produce the same expression: the algorithm is blind to the colors.

The scene of Figure 1 #

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inductive WesterbeekKoolenMaes2015.Object :
Type

The objects of a scene: the tomato and the distractors of other types.

Instances For
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    @[instance_reducible]
    instance WesterbeekKoolenMaes2015.instDecidableEqObject :
    DecidableEq Object
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    def WesterbeekKoolenMaes2015.instReprObject.repr :
    Object → 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 WesterbeekKoolenMaes2015.instReprObject :
      Repr Object
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      inductive WesterbeekKoolenMaes2015.ObjectValue :
      Type

      Types and colors.

      Instances For
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        @[instance_reducible]
        instance WesterbeekKoolenMaes2015.instDecidableEqObjectValue :
        DecidableEq ObjectValue
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        @[instance_reducible]
        instance WesterbeekKoolenMaes2015.instReprObjectValue :
        Repr ObjectValue
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        def WesterbeekKoolenMaes2015.instReprObjectValue.repr :
        ObjectValue → 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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          def WesterbeekKoolenMaes2015.scene (tomatoColor : ObjectValue) :
          DaleReiter1995.KB Object DaleReiter1995.Attr ObjectValue

          The scene, with the tomato in a given color.

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          Instances For
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            theorem WesterbeekKoolenMaes2015.tomato_bare (tomatoColor : ObjectValue) :
            (DaleReiter1995.Domain.flat (scene tomatoColor) DaleReiter1995.Attr.type).makeReferringExpression Object.tomato {Object.pineapple, Object.cucumber} [DaleReiter1995.Attr.type, DaleReiter1995.Attr.property Degree.PropertyDomain.color] = some {(DaleReiter1995.Attr.type, ObjectValue.tomato)}

            Color first or type first, the algorithm says the tomato of the yellow tomato as of the red one.

            The decision rule #

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            def WesterbeekKoolenMaes2015.DecisionRule (rate : ℚ → ℚ) :
            Prop

            The paper's decision rule: the rate of mentioning a color falls strictly with the color's typicality score for the object.

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            Instances For
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              theorem WesterbeekKoolenMaes2015.decision_rule_not_ia (c : ℚ) :
              ¬DecisionRule fun (x : ℚ) => c

              A constant rate, the Incremental Algorithm's, does not follow the rule.