Documentation

Eval.Homogeneity.Account

Accounts of homogeneity #

A sentence with a plural definite is homogeneous: the triangles are blue is true when all of them are, false when none is, and neither true nor false in between. Each account gives a sentence, under the quantifier that embeds the definite, a verdict on a display of each individual's count of objects with the property. Five accounts are context-free: four in the statements of Križ and Chemla, who assess them, Spector's supervaluation over the existential and the universal resolution of the definite, the same supervaluation over each individual's resolution, the literal meaning against its global exhaustification after Magri, and the universal projection of a homogeneity presupposition after Löbner and Gajewski; and Križ and Spector's candidate interpretations, each individual's plurality taking its own candidate domain (Account.value). Four depend on the question a context raises: in the statements of Augurzky et al., Križ's non-implicature approach, on which the context resolves the gap, Bar-Lev's implicature approach, on which pruning the alternatives yields non-maximality outside downward-entailing scopes, and that approach with the scalar implicature of not every, as Augurzky et al. amend it; and in the statement of Romoli et al., Guerrini and Wehbe's presuppositional exhaustification below the quantifier, its homogeneity presupposition projected by Strong Kleene and accommodated globally (Account.accepts).

TODO #

Križ and Spector's non-maximality, from the candidates strongly relevant to the issue, is not stated on Augurzky et al.'s pictures, so they are silent there.

Bar-Lev's own statement of his account (Studies.BarLev2021) reaches Križ and Chemla's displays unembedded and under negation only, so his account is scored here as Augurzky et al. state it, under every, no and not every; under exactly two it is silent, Romoli et al. counting Guerrini and Wehbe's the only account stated for non-monotonic quantifiers.

References #

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inductive Eval.Homogeneity.Account :
Type

The accounts of homogeneity.

  • supervaluation : Account

    [Spe13b]'s supervaluation over the existential and the universal resolution.

  • pointwise : Account

    The supervaluation over each individual's resolution.

  • krizSpector : Account

    [KS21b]'s candidate interpretations, each plurality taking its own candidate domain.

  • exhaustification : Account

    The literal meaning against its global exhaustification, after [Mag14].

  • presupposition : Account

    The universal projection of a homogeneity presupposition, after [Lob00] and [Gaj05].

  • nonImplicature : Account

    [Kri16]'s non-implicature approach, on which the question a context raises resolves the gap.

  • implicature : Account

    [BL21]'s implicature approach, on which pruning yields non-maximality outside downward-entailing scopes.

  • implicatureEnriched : Account

    The implicature approach with the scalar implicature of not every, as [ABB+23] amend it.

  • presuppositionalExhaustification : Account

    [GW25c]'s presuppositional exhaustification below the quantifier, its homogeneity presupposition projected by Strong Kleene and accommodated globally, as [RSA+26] state it.

Instances For
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    @[instance_reducible]
    instance Eval.Homogeneity.instDecidableEqAccount :
    DecidableEq Account
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    def Eval.Homogeneity.instReprAccount.repr :
    Account → 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 Eval.Homogeneity.instReprAccount :
      Repr Account
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      def Eval.Homogeneity.Account.value (a : Account) (q : Quantifier.NumberTree) [DecidableRel q] (counts : List ℕ) :
      Option SignType

      The value a context-free account gives a sentence under a quantifier, on a display of each individual's count of objects with the property, by the account's own definition; none for an account that needs a context.

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        def Eval.Homogeneity.Account.accepts (a : Account) (q : RomoliEtAl2026.Quantifier) (ctx : AugurzkyEtAl2023.Context) (counts : List ℕ) :
        Option Bool

        Whether an account accepts a sentence under one of [RSA+26]'s quantifiers on a display in a context, where linglib states it. A context-free account accepts the sentence where it makes it true, and the others decide by their own definitions, the implicature approach only under the quantifiers [ABB+23] state it for.

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        Instances For