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Linglib.Theories.Semantics.Modality.Ability

Ability Modals: Kratzer Bridge #

@cite{hacquard-2006} @cite{kratzer-1981} @cite{nadathur-2023}

Connects the causal model of ability (CausalFrame World with actualization = .aspectual, defined in ComplementEntailing.lean) to Kratzer's modal semantics.

The core semantics of ability modals — abilityFrame, sufficientAt, actualityWithAspect, and all actuality-entailment theorems — live in Causation/ComplementEntailing.lean. This file provides only the bridge to Kratzer's circumstantial possibility.

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def Nadathur2023.Ability.toCircumstantialBase (f : CausalVerb.CausalFrame Semantics.Attitudes.Intensional.World) :
Semantics.Modality.Kratzer.ModalBase

Convert an ability CausalFrame to a Kratzer circumstantial modal base.

The modal base at each world returns propositions encoding the causal background. Ability IS circumstantial possibility, where the "circumstances" are the causal structure.

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    def Nadathur2023.Ability.abilityAsKratzerPossibility (f : CausalVerb.CausalFrame Semantics.Attitudes.Intensional.World) (w : Semantics.Attitudes.Intensional.World) :
    Bool

    Ability as Kratzer possibility: "can VP" is ◇(complement) where the modal base encodes circumstantial facts.

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    • One or more equations did not get rendered due to their size.
    Instances For
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      theorem Nadathur2023.Ability.ability_is_causal_sufficiency (f : CausalVerb.CausalFrame Semantics.Attitudes.Intensional.World) (w : Semantics.Attitudes.Intensional.World) :
      f.sufficientAt w = Core.StructuralEquationModel.causallySufficient f.dynamics (f.background w) f.trigger f.complement

      Ability = causal sufficiency (definitional).