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Studies.VanDerWouden1997

van der Wouden (1997): Negative Contexts: Collocation, Polarity and Multiple Negation #

Van der Wouden ranks negative contexts by strength, monotone decreasing, anti-additive and antimorphic, and classes polarity items by the weakest context that licenses or blocks them. Dutch ooit 'ever' is his bipolar element: a weak negative polarity item, out in a clause that is not monotone decreasing and fine under weinig 'few' and geen van 'none of', and a weak positive polarity item, blocked by the antimorphic negation niet. The library's contexts for these operators have the strengths he assigns them (context_strengths). He holds that a verb with negative properties is anti-additive, none being only monotone decreasing; deny bears this out, but doubt, on his own sketch of it as not believing the complement, is only monotone decreasing (verb_strengths). With ooit's Fragment entry every judgment of his (184) is the licensing theory's (judgments_predicted). An entry that were only a negative polarity item, as on the analysis with two items ooit, would be admitted under niet, against (184d) (negativeOnly_admits_niet).

References #

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inductive VanDerWouden1997.Context :
Type

The contexts of (184), a positive clause, weinig 'few', geen van 'none of' and niet.

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    @[instance_reducible]
    instance VanDerWouden1997.instDecidableEqContext :
    DecidableEq Context
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    def VanDerWouden1997.instReprContext.repr :
    Context → 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 VanDerWouden1997.instReprContext :
      Repr Context
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      def VanDerWouden1997.Context.Admits :
      Context → PolarityItem → Prop

      A positive clause admits the items that need no licensing, and each operator admits what its licensing context admits.

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        @[instance_reducible]
        instance VanDerWouden1997.instDecidablePredPolarityItemAdmits (c : Context) :
        DecidablePred c.Admits
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        theorem VanDerWouden1997.context_strengths :
        PolarityItem.LicensingContext.few.licenser.Holds NaturalLogic.Signature.anti ∧ ¬PolarityItem.LicensingContext.few.licenser.Holds NaturalLogic.Signature.antiAdd ∧ PolarityItem.LicensingContext.nobody.licenser.Holds NaturalLogic.Signature.antiAdd ∧ ¬PolarityItem.LicensingContext.nobody.licenser.Holds NaturalLogic.Signature.antiAddMult ∧ PolarityItem.LicensingContext.negation.licenser.Holds NaturalLogic.Signature.antiAddMult

        Weinig is monotone decreasing and not anti-additive, geen van anti-additive and not antimorphic, and niet antimorphic.

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        theorem VanDerWouden1997.verb_strengths :
        PolarityItem.LicensingContext.denyVerb.licenser.Holds NaturalLogic.Signature.antiAdd ∧ ¬PolarityItem.LicensingContext.denyVerb.licenser.Holds NaturalLogic.Signature.antiAddMult ∧ PolarityItem.LicensingContext.doubtVerb.licenser.Holds NaturalLogic.Signature.anti ∧ ¬PolarityItem.LicensingContext.doubtVerb.licenser.Holds NaturalLogic.Signature.antiAdd

        Van der Wouden holds that a verb with negative properties is anti-additive, no verb being only monotone decreasing. Deny bears this out, being anti-additive and not antimorphic. Doubt, on his sketch of it as not believing that the complement is true, which is the library's model of it, is monotone decreasing and not anti-additive.

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        def VanDerWouden1997.Context.ofKey :
        String → Option Context

        The context a row's class names.

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          theorem VanDerWouden1997.judgments_predicted (d : Datum) :
          d ∈ Examples.all → d.feature? "item" = some "ooit" ∧ ∃ c ∈ (d.feature? "context").bind Context.ofKey, d.judgment = Judgment.acceptable ↔ c.Admits Dutch.PolarityItems.ooit

          Every row of (184) is on ooit, names its context, and is acceptable exactly when the context admits ooit's Fragment entry.

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          theorem VanDerWouden1997.negativeOnly_admits_niet :
          Context.niet.Admits (have __src := Dutch.PolarityItems.ooit; { form := __src.form, licensor := __src.licensor, freeChoice := __src.freeChoice, licensingContexts := __src.licensingContexts, excludedContexts := __src.excludedContexts })

          A negative polarity item that is not also a positive one, as on the analysis with two items ooit, is admitted under niet.