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Linglib.Phenomena.Modality.Studies.Kratzer2012Practical

Practical Reasoning — @cite{kratzer-2012} §2.8 #

Teleological modality: "To get to Harlem, you have to take the A train."

The scenario illustrates how goal-directed reasoning arises from Kratzer's ordering source. The circumstantial modal base includes all four worlds; the goal ordering restricts to worlds where the goal is achieved. Since every goal-reaching world involves the A train, taking the A train is a teleological necessity.

WorldReachesGoalTakesATrainNotes
w0yesyesA train, no delay
w1yesyesA train, with delay
w2nonoTakes bus
w3nonoStays home

Reference: Kratzer, A. (2012). Modals and Conditionals. OUP. Ch. 2 §2.8.

Propositions #

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def Phenomena.Modality.PracticalReasoningBridge.reachesGoal :
BProp Semantics.Attitudes.Intensional.World

The agent reaches Harlem (the goal).

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    def Phenomena.Modality.PracticalReasoningBridge.takesATrain :
    BProp Semantics.Attitudes.Intensional.World

    The agent takes the A train.

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      def Phenomena.Modality.PracticalReasoningBridge.noDelay :
      BProp Semantics.Attitudes.Intensional.World

      No delay (distinguishes w0 from w1).

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        Conversational backgrounds #

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        def Phenomena.Modality.PracticalReasoningBridge.circumstantialBase :
        Semantics.Modality.Kratzer.ModalBase

        Circumstantial modal base: all worlds accessible (empty fact set).

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          def Phenomena.Modality.PracticalReasoningBridge.goalOrdering :
          Semantics.Modality.Kratzer.OrderingSource

          Goal ordering source: ranks worlds by whether the goal is reached.

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            def Phenomena.Modality.PracticalReasoningBridge.efficiencyOrdering :
            Semantics.Modality.Kratzer.OrderingSource

            Efficiency ordering: ranks by goal AND no-delay. w0 > w1.

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              Teleological flavor structure #

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              def Phenomena.Modality.PracticalReasoningBridge.harlemTeleological :
              Semantics.Modality.Kratzer.TeleologicalFlavor

              Harlem scenario as a Kratzer teleological flavor.

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                Theory-neutral facts #

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                theorem Phenomena.Modality.PracticalReasoningBridge.goal_worlds_all_take_a :
                (Semantics.Attitudes.Intensional.allWorlds.all fun (w : Semantics.Attitudes.Intensional.World) => !reachesGoal w || takesATrain w) = true

                Every world that reaches the goal also takes the A train.

                Derivation theorems #

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                theorem Phenomena.Modality.PracticalReasoningBridge.teleological_necessity (w : Semantics.Attitudes.Intensional.World) :
                Semantics.Modality.Kratzer.necessity circumstantialBase goalOrdering takesATrain w = true

                Teleological necessity: Given the goal ordering, the A train is necessary. Best worlds = {w0, w1} (goal-reaching), both take the A train.

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                theorem Phenomena.Modality.PracticalReasoningBridge.unrestricted_not_necessary (w : Semantics.Attitudes.Intensional.World) :
                Semantics.Modality.Kratzer.necessity circumstantialBase Semantics.Modality.Kratzer.emptyBackground takesATrain w = false

                Without goal restriction, A train is not necessary. With empty ordering, all worlds are best, and w2/w3 don't take the A train.

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                theorem Phenomena.Modality.PracticalReasoningBridge.efficiency_refines (w : Semantics.Attitudes.Intensional.World) :
                Semantics.Modality.Kratzer.necessity circumstantialBase efficiencyOrdering takesATrain w = true

                Efficiency refines: Adding a no-delay criterion still yields necessity. Best worlds = {w0} (goal + no delay), and w0 takes the A train.

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                theorem Phenomena.Modality.PracticalReasoningBridge.harlem_uses_teleological :
                Semantics.Modality.Kratzer.TeleologicalFlavor.flavorTag = Core.Modality.ModalFlavor.circumstantial

                Teleological uses circumstantial flavor tag.