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Linglib.Discourse.Centering.Rule2

Centering Theory — Rule 2 (Transition Preference) #

[GJW95] [BFP87] [Str98] [PSDEH04] Two Rule 2 variants in this file: GJW 95 sequence ranking (CON-CON > RET-RET > SHIFT-SHIFT) via pairRank, and Strube 1998's cheap/expensive distinction via isCheap. The BFP 87 4-way variant lives in Studies/PoesioEtAl2004.lean.

Rule 2 (GJW 1995): sequences of transitions #

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def Discourse.Centering.pairRank (t₁ t₂ : Transition) :
ℕ

Rule 2 (GJW 95): sequence preference by sum-of-ranks.

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    theorem Discourse.Centering.rule2_continuations_preferred_over_retentions :
    pairRank Transition.continuation Transition.continuation > pairRank Transition.retaining Transition.retaining
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    theorem Discourse.Centering.rule2_retentions_preferred_over_shifts :
    pairRank Transition.retaining Transition.retaining > pairRank Transition.shifting Transition.shifting
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    theorem Discourse.Centering.rule2_continuations_preferred_over_shifts :
    pairRank Transition.continuation Transition.continuation > pairRank Transition.shifting Transition.shifting

    Rule 2 (Strube 1998): cheap vs expensive #

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    def Discourse.Centering.isCheap {E : Type u_1} {R : Type u_2} [DecidableEq E] [CfRankerOf E R] {U : Type u_3} [Realizes U E] (prev : Utterance E R) (cur : U) (prevCp : Option E) :
    Prop

    A transition is cheap ([Str98]) if CB(U_n) = CP(U_{n-1}): the previous utterance's preferred center predicts the current CB.

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      @[implicit_reducible]
      instance Discourse.Centering.isCheap.decidable {E : Type u_1} {R : Type u_2} [DecidableEq E] [CfRankerOf E R] {U : Type u_3} [Realizes U E] (prev : Utterance E R) (cur : U) (prevCp : Option E) :
      Decidable (isCheap prev cur prevCp)
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      def Discourse.Centering.Rule2Strube1998Preferred {E : Type u_1} {R : Type u_2} [DecidableEq E] [CfRankerOf E R] {U : Type u_3} [Realizes U E] (prev : Utterance E R) (cur : U) (prevCp : Option E) :
      Prop

      Strube 1998 Rule 2 preference: cheap > expensive.

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