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Studies.Rakosi2019

Rákosi (2019): Reciprocal anaphors in singular constructions in Hungarian #

This file formalizes [Rak19]: the reciprocal egymás takes any antecedent that denotes a plurality, whether or not the plurality is coded morphosyntactically, while a plural reflexive requires a plural antecedent and a plural verb. Over the paper's examples, a reciprocal is acceptable exactly when its antecedent is semantically plural (reciprocal_iff_semanticPlural), a plural reflexive exactly when the verb agrees in the plural (reflexivePl_iff_verb_pl), and a singular reflexive exactly when it agrees in the singular (reflexiveSg_iff_verb_sg); each of the four constructions with a singular verb, the quantified antecedents of §3, the singular coordinate noun phrases of §4, the collective nouns of §5 and the pro-dropped singular variables of §6, licenses the reciprocal (reciprocal_with_singular_verb). The inclusive reflexive of §2 is set apart: it is never read as a bound variable (inclusive_not_bound), so it is no counterexample, and the reciprocal is excluded in its construction. The semantic side is the plural-assignment semantics of PPCDRT: reciprocity at a jointly defined state makes the antecedent denote two or more individuals (reciprocity_implies_multiple_individuals), the plurality a reciprocal feeds on, whereas binding is satisfied by a singleton state (binding_compatible_with_singleton), which is why a reflexive's plurality is a matter of φ-agreement instead. The reciprocal itself carries no number feature (egymas_no_number_feature), the reflexive inflects (reflexive_number_paradigm).

References #

The rows #

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inductive Rakosi2019.Anaphor :
Type

The anaphor of a row: the reciprocal, a singular or plural reflexive bound by its antecedent, or the inclusive reflexive of §2.

Instances For
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    @[instance_reducible]
    instance Rakosi2019.instDecidableEqAnaphor :
    DecidableEq Anaphor
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    def Rakosi2019.anaphor? (e : Datum) :
    Option Anaphor

    The anaphor a row records.

    Equations
    • One or more equations did not get rendered due to their size.
    Instances For
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      def Rakosi2019.VerbPlural (e : Datum) :
      Prop

      The verb agrees in the plural.

      Equations
      Instances For
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        def Rakosi2019.SemanticPlural (e : Datum) :
        Prop

        The antecedent denotes a plurality.

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        Instances For
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          @[instance_reducible]
          instance Rakosi2019.instDecidableVerbPlural (e : Datum) :
          Decidable (VerbPlural e)
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          @[instance_reducible]
          instance Rakosi2019.instDecidableSemanticPlural (e : Datum) :
          Decidable (SemanticPlural e)
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          The asymmetry #

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          theorem Rakosi2019.reciprocal_iff_semanticPlural (e : Datum) :
          e ∈ Examples.all → anaphor? e = some Anaphor.reciprocal → (e.judgment = Judgment.acceptable ↔ SemanticPlural e)

          A reciprocal is acceptable exactly when its antecedent is semantically plural.

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          theorem Rakosi2019.reflexivePl_iff_verb_pl (e : Datum) :
          e ∈ Examples.all → anaphor? e = some Anaphor.reflexivePl → (e.judgment = Judgment.acceptable ↔ VerbPlural e)

          A plural reflexive is acceptable exactly when the verb agrees in the plural.

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          theorem Rakosi2019.reflexiveSg_iff_verb_sg (e : Datum) :
          e ∈ Examples.all → anaphor? e = some Anaphor.reflexiveSg → (e.judgment = Judgment.acceptable ↔ ¬VerbPlural e)

          A singular reflexive is acceptable exactly when the verb agrees in the singular.

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          theorem Rakosi2019.reciprocal_with_singular_verb (c : String) :
          c ∈ ["quantified", "coordinate", "collective", "boundPro"] → ∃ e ∈ Examples.all, e.feature? "antecedent" = some c ∧ anaphor? e = some Anaphor.reciprocal ∧ ¬VerbPlural e ∧ e.judgment = Judgment.acceptable

          Each of the four constructions of §§3–6 licenses the reciprocal under a singular verb.

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          theorem Rakosi2019.inclusive_not_bound (e : Datum) :
          e ∈ Examples.all → anaphor? e = some Anaphor.inclusiveReflexive → List.lookup "bound variable" e.readings ≠ some Judgment.acceptable

          The inclusive reflexive of §2 is never read as a bound variable, so it is no plural reflexive with a singular antecedent.

          The semantics of the two anaphoric relations #

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          theorem Rakosi2019.reciprocity_implies_multiple_individuals {E : Type u_1} {uAnaph uAnt : ℕ} {S : PluralAssign ℕ E} {Δ : Set ℕ} (hdef : ∃ s ∈ S, s uAnaph ≠ ⊥ ∧ s uAnt ≠ ⊥) (h : PPCDRT.reciprocityCond uAnaph uAnt S Δ) :
          (PCDRT.value uAnt S).Nontrivial

          Reciprocity at a state where both discourse referents are defined makes the antecedent denote two or more individuals, under any distribution. This is the plurality a reciprocal requires of its antecedent.

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          theorem Rakosi2019.binding_compatible_with_singleton {E : Type u_1} (e : E) (uAnaph uAnt : ℕ) :
          PPCDRT.bindingCond uAnaph uAnt {(PartialAssign.single uAnaph e).update uAnt e} ∅

          Binding is satisfied by a singleton state mapping both discourse referents to one value: reflexive binding imposes no plurality on the denotation.

          The forms #

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          theorem Rakosi2019.egymas_no_number_feature :
          Hungarian.Reciprocals.egymas.number = none

          egymás is invariable: it bears no number feature, consistent with a plurality requirement that is semantic rather than a matter of agreement.

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          theorem Rakosi2019.reflexive_number_paradigm :
          Hungarian.Reciprocals.maga.number = some Number.singular ∧ Hungarian.Reciprocals.maguk.number = some Number.plural

          The reflexive inflects for number, maga against maguk, and must match the verb.