Documentation

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.

Propositions #

source
def Phenomena.Modality.InformationalBackgroundsBridge.raining :
BProp Semantics.Attitudes.Intensional.World

It is raining.

Equations
Instances For
    source
    def Phenomena.Modality.InformationalBackgroundsBridge.reportSaysRain :
    BProp Semantics.Attitudes.Intensional.World

    The weather report says it is raining.

    Equations
    Instances For

      Conversational backgrounds #

      source
      def Phenomena.Modality.InformationalBackgroundsBridge.informationalBg :
      Semantics.Modality.Kratzer.ModalBase

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

      Equations
      Instances For
        source
        def Phenomena.Modality.InformationalBackgroundsBridge.reliabilityAssumption :
        BProp Semantics.Attitudes.Intensional.World

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

        Equations
        • One or more equations did not get rendered due to their size.
        Instances For
          source
          def Phenomena.Modality.InformationalBackgroundsBridge.strongEpistemicBg :
          Semantics.Modality.Kratzer.ModalBase

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

          Equations
          • One or more equations did not get rendered due to their size.
          Instances For

            Derivation theorems #

            source
            theorem Phenomena.Modality.InformationalBackgroundsBridge.informational_alone_not_necessity (w : Semantics.Attitudes.Intensional.World) :
            Semantics.Modality.Kratzer.necessity informationalBg Semantics.Modality.Kratzer.emptyBackground raining w = false

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

            source
            theorem Phenomena.Modality.InformationalBackgroundsBridge.with_reliability_necessity (w : Semantics.Attitudes.Intensional.World) :
            Semantics.Modality.Kratzer.necessity strongEpistemicBg Semantics.Modality.Kratzer.emptyBackground raining w = true

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

            source
            theorem Phenomena.Modality.InformationalBackgroundsBridge.informational_not_realistic :
            ¬Semantics.Modality.Kratzer.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.

            source
            theorem Phenomena.Modality.InformationalBackgroundsBridge.strong_epistemic_not_realistic :
            ¬Semantics.Modality.Kratzer.isRealistic strongEpistemicBg

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

            source
            theorem Phenomena.Modality.InformationalBackgroundsBridge.informational_possibility (w : Semantics.Attitudes.Intensional.World) :
            Semantics.Modality.Kratzer.possibility informationalBg Semantics.Modality.Kratzer.emptyBackground raining w = true

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

            Evidence type bridge #

            source
            def Phenomena.Modality.InformationalBackgroundsBridge.reportEvidence :
            Core.Evidence.EvidentialSource

            The weather report is hearsay evidence.

            Equations
            Instances For
              source
              theorem Phenomena.Modality.InformationalBackgroundsBridge.report_is_retrospective :
              reportEvidence.toEvidentialPerspective = Core.Evidence.EvidentialPerspective.retrospective

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