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Linglib.Phenomena.Modality.Studies.Kratzer2012Informational

Informational Backgrounds — @cite{kratzer-2012} §2.3d #

Epistemic modals with an informational (potentially non-realistic) modal base.

A weather report provides evidence for rain, but the report can be wrong: the proposition "the report says rain" does not guarantee rain is actual. This makes the informational background non-realistic — the actual world may not be in ∩f(w) if the report is wrong at that world.

WorldRainingReportSaysRainNotes
w0yesyesReport correct
w1yesnoRain, report missed
w2noyesDry, report wrong
w3nonoBoth correct

Reference: Kratzer, A. (2012). Modals and Conditionals. OUP. Ch. 2 §2.3d.

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@[reducible, inline]
abbrev Phenomena.Modality.InformationalBackgroundsBridge.World :
Type
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    Propositions #

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    def Phenomena.Modality.InformationalBackgroundsBridge.raining :
    World → Prop

    It is raining.

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      @[implicit_reducible]
      instance Phenomena.Modality.InformationalBackgroundsBridge.instDecidablePredWorldRaining :
      DecidablePred raining
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      def Phenomena.Modality.InformationalBackgroundsBridge.reportSaysRain :
      World → Prop

      The weather report says it is raining.

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        @[implicit_reducible]
        instance Phenomena.Modality.InformationalBackgroundsBridge.instDecidablePredWorldReportSaysRain :
        DecidablePred reportSaysRain
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        Conversational backgrounds #

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        def Phenomena.Modality.InformationalBackgroundsBridge.informationalBg :
        Core.Logic.Intensional.ModalBase World

        Informational modal base: accessible worlds are those where the report says rain. Accessible = {w0, w2}.

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          def Phenomena.Modality.InformationalBackgroundsBridge.reliabilityAssumption :
          World → Prop

          Reliability assumption: if the report says rain, it's raining. This is a conditional proposition (report → rain).

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            def Phenomena.Modality.InformationalBackgroundsBridge.strongEpistemicBg :
            Core.Logic.Intensional.ModalBase World

            Strong epistemic base: report + reliability. Accessible = {w0} only.

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              Derivation theorems #

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              theorem Phenomena.Modality.InformationalBackgroundsBridge.informational_alone_not_necessity (w : World) :
              ¬Semantics.Modality.Kratzer.necessity informationalBg Core.Logic.Intensional.emptyBackground raining w

              Report alone doesn't entail rain. The informational base gives accessible worlds {w0, w2}, and raining is false at w2.

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              theorem Phenomena.Modality.InformationalBackgroundsBridge.with_reliability_necessity (w : World) :
              Semantics.Modality.Kratzer.necessity strongEpistemicBg Core.Logic.Intensional.emptyBackground raining w

              Report + reliability entails rain. The strong base gives accessible worlds {w0}, and raining is true at w0.

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              theorem Phenomena.Modality.InformationalBackgroundsBridge.informational_not_realistic :
              ¬Core.Logic.Intensional.isRealistic informationalBg

              The informational base is not realistic. At w1 (it rains but the report doesn't say so), w1 ∉ ∩f(w1) because reportSaysRain w1 = false.

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              theorem Phenomena.Modality.InformationalBackgroundsBridge.strong_epistemic_not_realistic :
              ¬Core.Logic.Intensional.isRealistic strongEpistemicBg

              The strong epistemic base is also not realistic. At w1, the report doesn't say rain, so w1 fails the reportSaysRain proposition.

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              theorem Phenomena.Modality.InformationalBackgroundsBridge.informational_possibility (w : World) :
              Semantics.Modality.Kratzer.possibility informationalBg Core.Logic.Intensional.emptyBackground raining w

              Possibility holds under report alone. Even without reliability, rain is possible (w0 is accessible and raining).

              Evidence type bridge #

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              def Phenomena.Modality.InformationalBackgroundsBridge.reportEvidence :
              Features.Evidentiality.EvidentialSource

              The weather report is hearsay evidence.

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                theorem Phenomena.Modality.InformationalBackgroundsBridge.report_is_retrospective :
                reportEvidence.toEvidentialPerspective = some Features.Evidentiality.EvidentialPerspective.retrospective

                Hearsay evidence is retrospective (the event precedes the report).