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Linglib.Phenomena.ScalarImplicatures.Studies.Katzir2007

Katzir 2007: Structurally-Defined Alternatives (End-to-End) #

@cite{katzir-2007}

Katzir, R. (2007). Structurally-defined alternatives. Linguistics and Philosophy, 30(6), 669–690.

Unified Tree Demonstration #

This file demonstrates that a single Tree Cat String supports both:

One tree, two interfaces — the Y-model made concrete.

The Argument #

  1. Build φ = "some student sleeps" as Tree Cat String with QR
  2. Generate φ' = "every student sleeps" via leafSubst (Det substitution)
  3. Interpret both: ⟦φ⟧ = true, ⟦φ'⟧ = false → asserting φ implicates ¬φ'
  4. Show φ contains no ConjP/NegP → symmetric alternative "some but not all" cannot be generated structurally

This is Katzir's solution to the symmetry problem: structural constraints on alternatives prevent the symmetric alternative from being generated, licensing the scalar implicature.

source
def Phenomena.ScalarImplicatures.Studies.Katzir2007.φ :
Core.Tree.Tree Core.Tree.Cat String

"Some student sleeps" after QR, with UD-grounded categories:

[S [DP [Det some] [N student]] [₁ [S [t₁:NP] [VP [V sleeps]]]]]
Equations
  • One or more equations did not get rendered due to their size.
Instances For
    source
    def Phenomena.ScalarImplicatures.Studies.Katzir2007.φ' :
    Core.Tree.Tree Core.Tree.Cat String

    Scalar alternative: substitute "some" → "every" at Det position. This is Katzir's core operation (def 19, substitution): replace a terminal with a same-category item from the substitution source. Both "some" and "every" are Det terminals in the lexicon.

    Equations
    Instances For
      source
      theorem Phenomena.ScalarImplicatures.Studies.Katzir2007.some_student_sleeps :
      Semantics.Composition.Tree.evalTree Semantics.Composition.QuantifierComposition.quantLex Semantics.Composition.QuantifierComposition.g₀ φ = some true

      "Some student sleeps" is true: John is a student and sleeps.

      source
      theorem Phenomena.ScalarImplicatures.Studies.Katzir2007.every_student_sleeps :
      Semantics.Composition.Tree.evalTree Semantics.Composition.QuantifierComposition.quantLex Semantics.Composition.QuantifierComposition.g₀ φ' = some false

      The scalar alternative "every student sleeps" is false: Mary is a student but doesn't sleep.

      source
      theorem Phenomena.ScalarImplicatures.Studies.Katzir2007.readings_differ :
      Semantics.Composition.Tree.evalTree Semantics.Composition.QuantifierComposition.quantLex Semantics.Composition.QuantifierComposition.g₀ φ ≠ Semantics.Composition.Tree.evalTree Semantics.Composition.QuantifierComposition.quantLex Semantics.Composition.QuantifierComposition.g₀ φ'

      The two readings differ: genuine scalar inference. Asserting "some" when "every" was available implicates ¬"every".

      The symmetry problem: for any stronger alternative φ' = "every", there exists a symmetric alternative φ'' = "some but not all" which is also stronger. Naïve exhaustivity would predict no implicature.

      Katzir's solution: φ'' requires ConjP and NegP structure, which cannot be generated from L(φ) = lexicon ∪ subtrees(φ) because the source tree φ contains neither category.

      source
      theorem Phenomena.ScalarImplicatures.Studies.Katzir2007.no_conjp :
      Core.Tree.Tree.containsCat Core.Tree.Cat.ConjP φ = false

      φ contains no ConjP anywhere in its structure.

      source
      theorem Phenomena.ScalarImplicatures.Studies.Katzir2007.no_negp :
      Core.Tree.Tree.containsCat Core.Tree.Cat.NegP φ = false

      φ contains no NegP anywhere in its structure.

      source
      theorem Phenomena.ScalarImplicatures.Studies.Katzir2007.subtrees_lack_conjp :
      (φ.subtrees.all fun (t : Core.Tree.Tree Core.Tree.Cat String) => !Core.Tree.Tree.containsCat Core.Tree.Cat.ConjP t) = true

      None of φ's subtrees contain ConjP either.