Documentation

Linglib.Phenomena.ScalarImplicatures.Hurford

RSA Analysis of Hurford's Constraint #

@cite{hurford-1974} @cite{singh-2008} @cite{potts-levy-2015}

Models Hurford's constraint as a consequence of speaker rationality in RSA.

Hurford's constraint: "#A or B" is infelicitous when A ⊆ B or B ⊆ A.

In RSA, felicity = speaker rationality. A speaker wouldn't say "A or B" if:

  1. One disjunct is redundant (B⊆A makes B add nothing)
  2. A simpler utterance (just "A") conveys the same information

The rescue by exhaustification works because:

Status #

The ℚ-based RSA evaluation infrastructure (RSA.Eval, boolToRat, LURSA) has been removed. Type definitions and semantic characterizations of redundancy are preserved. RSA computations (L1, S1) need to be re-implemented using the new RSAConfig framework.

Model #

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@[reducible, inline]
abbrev Phenomena.ScalarImplicatures.Hurford.HWorld :
Type

World states for Hurford scenarios use the canonical SomeAllWorld from Phenomena.ScalarImplicatures.Basic: .none (nothing read), .someNotAll (some-but-not-all read), .all (all read).

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    inductive Phenomena.ScalarImplicatures.Hurford.HUtterance :
    Type

    Utterances for Hurford disjunction scenarios.

    Key utterances:

    • some_: "Mary read some of the books"
    • all_: "Mary read all of the books"
    • someOrAll: "Mary read some or all of the books"
    • null: Null/silence alternative
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      @[implicit_reducible]
      instance Phenomena.ScalarImplicatures.Hurford.instDecidableEqHUtterance :
      DecidableEq HUtterance
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      @[implicit_reducible]
      instance Phenomena.ScalarImplicatures.Hurford.instReprHUtterance :
      Repr HUtterance
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      def Phenomena.ScalarImplicatures.Hurford.instReprHUtterance.repr :
      HUtterance → ℕ → Std.Format
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        @[implicit_reducible]
        instance Phenomena.ScalarImplicatures.Hurford.instInhabitedHUtterance :
        Inhabited HUtterance
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        def Phenomena.ScalarImplicatures.Hurford.instInhabitedHUtterance.default :
        HUtterance
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          def Phenomena.ScalarImplicatures.Hurford.lexBaseMeaning :
          HUtterance → HWorld → Bool

          Base lexicon: "some" = at-least-one (weak reading).

          Under this lexicon:

          • "some" is true in {someNotAll, all_}
          • "all" is true only in {all_}
          • "some or all" = "some" ∨ "all" = "some" (since all⊆some)

          This makes "some or all" redundant -- a Hurford violation.

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            def Phenomena.ScalarImplicatures.Hurford.lexRefinedMeaning :
            HUtterance → HWorld → Bool

            Refined lexicon: "some" = some-but-not-all (exhaustified reading).

            Under this lexicon:

            • "some" is true only in {someNotAll}
            • "all" is true only in {all_}
            • "some or all" is now informative: covers {someNotAll, all_}

            This rescues the Hurford violation -- the disjunction is no longer redundant.

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              def Phenomena.ScalarImplicatures.Hurford.someOrAllTrueWorlds_base :
              List HWorld

              Worlds where "some or all" is true under base lexicon

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                def Phenomena.ScalarImplicatures.Hurford.someTrueWorlds_base :
                List HWorld

                Worlds where "some" is true under base lexicon

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                  theorem Phenomena.ScalarImplicatures.Hurford.base_redundancy :
                  someOrAllTrueWorlds_base = someTrueWorlds_base

                  Under base lexicon, "some or all" and "some" have the same extension. This is the semantic redundancy that causes Hurford violations.

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                  def Phenomena.ScalarImplicatures.Hurford.someOrAllTrueWorlds_refined :
                  List HWorld

                  Worlds where "some or all" is true under refined lexicon

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                    def Phenomena.ScalarImplicatures.Hurford.someTrueWorlds_refined :
                    List HWorld

                    Worlds where "some" is true under refined lexicon

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                      theorem Phenomena.ScalarImplicatures.Hurford.refined_disjunction_informative :
                      someOrAllTrueWorlds_refined.length > someTrueWorlds_refined.length

                      Under refined lexicon, "some or all" covers more worlds than "some" alone. This is why the disjunction is informative and the Hurford violation is rescued.

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                      theorem Phenomena.ScalarImplicatures.Hurford.hurford_model_captures_rescue :
                      someOrAllTrueWorlds_refined.length > someTrueWorlds_refined.length ∧ someOrAllTrueWorlds_base = someTrueWorlds_base

                      Connection to empirical Hurford data.

                      The model predicts:

                      1. Hurford violations (e.g., "American or Californian") = low S1 probability because the disjunction is redundant under the natural reading

                      2. Rescued cases (e.g., "some or all") = higher S1 probability when the listener interprets with the refined lexicon (exh applied)

                      The prediction: felicitous iff the disjunction is informative under some lexicon.

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                      inductive Phenomena.ScalarImplicatures.Hurford.HyponymWorld :
                      Type

                      Worlds for hyponymy scenario

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                        @[implicit_reducible]
                        instance Phenomena.ScalarImplicatures.Hurford.instDecidableEqHyponymWorld :
                        DecidableEq HyponymWorld
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                        @[implicit_reducible]
                        instance Phenomena.ScalarImplicatures.Hurford.instReprHyponymWorld :
                        Repr HyponymWorld
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                        def Phenomena.ScalarImplicatures.Hurford.instReprHyponymWorld.repr :
                        HyponymWorld → ℕ → Std.Format
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                          @[implicit_reducible]
                          instance Phenomena.ScalarImplicatures.Hurford.instInhabitedHyponymWorld :
                          Inhabited HyponymWorld
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                          def Phenomena.ScalarImplicatures.Hurford.instInhabitedHyponymWorld.default :
                          HyponymWorld
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                            inductive Phenomena.ScalarImplicatures.Hurford.HyponymUtterance :
                            Type

                            Utterances for hyponymy scenario

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                              @[implicit_reducible]
                              instance Phenomena.ScalarImplicatures.Hurford.instDecidableEqHyponymUtterance :
                              DecidableEq HyponymUtterance
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                              @[implicit_reducible]
                              instance Phenomena.ScalarImplicatures.Hurford.instReprHyponymUtterance :
                              Repr HyponymUtterance
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                              def Phenomena.ScalarImplicatures.Hurford.instReprHyponymUtterance.repr :
                              HyponymUtterance → ℕ → Std.Format
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                                def Phenomena.ScalarImplicatures.Hurford.instInhabitedHyponymUtterance.default :
                                HyponymUtterance
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                                  @[implicit_reducible]
                                  instance Phenomena.ScalarImplicatures.Hurford.instInhabitedHyponymUtterance :
                                  Inhabited HyponymUtterance
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                                  def Phenomena.ScalarImplicatures.Hurford.lexHyponymMeaning :
                                  HyponymUtterance → HyponymWorld → Bool

                                  Lexicon for hyponymy: Californian ⊆ American (no refinement possible).

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                                    def Phenomena.ScalarImplicatures.Hurford.americanOrCalifornianTrueWorlds :
                                    List HyponymWorld

                                    Worlds where "American or Californian" is true

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                                      def Phenomena.ScalarImplicatures.Hurford.americanTrueWorlds :
                                      List HyponymWorld

                                      Worlds where "American" alone is true

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                                        theorem Phenomena.ScalarImplicatures.Hurford.hyponym_always_redundant :
                                        americanOrCalifornianTrueWorlds = americanTrueWorlds

                                        For hyponymy, the disjunction is always redundant -- no rescue possible.