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Linglib.Studies.Anaphora.AsherLascarides2003

Asher & Lascarides 2003: SDRT Right Frontier Constraint worked example #

@cite{asher-lascarides-2003}

Example (21) from p. 149 — the discourse where the book explicitly enumerates which attachment sites are available under the Right Frontier Constraint, and which are excluded. We replicate it against the SDRT substrate to verify that availableAttachmentPoints returns exactly the book-predicted set.

The example (21), p. 149 #

π₀:
  ├─ π₃, π₄
  │  ├─ π₃: K_π₃
  │  ├─ ⇓(π₃, π₄)              ← subordinating topic relation
  │  └─ π₄:
  │     ├─ π₁, π₂
  │     ├─ π₁: K_π₁
  │     ├─ π₂: K_π₂
  │     └─ Background(π₁, π₂)   ← coordinating

Reading the labelling F:

What the book asserts (p. 149) #

"assuming that π₂ in (21) is LAST, the available attachment sites are π₂ (by condition 1), π₄ (by condition 2a), π₃ (by condition 2b and 3) and π₀ (by condition 3). But π₁ is not available."

Why π₁ is not available #

π₁ and π₂ are siblings under Background, which is coordinating (not subordinating). After attaching to π₂ (LAST), the only way to reach π₁ would be through a subordinating relation — but Background doesn't qualify. Walking up via outscoping reaches π₄ (which contains both π₁ and π₂), and from π₄ we reach π₃ via the subordinating ⇓ relation. But π₁ is on the wrong side of a coordinating sibling boundary.

Substrate note #

@cite{asher-lascarides-2003}'s ⇓ topic-relation is not in the substrate's RhetoricalRelation enum (it's a structural relation the book uses informally; the headline truth-conditional inventory is Narration / Elaboration / Explanation / Result / Background / Contrast / Parallel + Consequence / Alternation / Correction). We encode ⇓ as .elaboration in the example below — both are subordinating, and the RFC's condition 2b only sees the isSubordinating projection. The example would behave identically with a hypothetical .topic constructor.

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abbrev Studies.Anaphora.AsherLascarides2003.Label :
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    abbrev Studies.Anaphora.AsherLascarides2003.Content :
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      def Studies.Anaphora.AsherLascarides2003.example21 :
      Discourse.SDRT.SDRS Label Content

      Example (21) from @cite{asher-lascarides-2003} p. 149, with LAST = π₂.

      Labels: 0 = π₀, 1 = π₁, 2 = π₂, 3 = π₃, 4 = π₄.

      Edges encode the labelled-discourse-structure conjuncts:

      • ⟨0, 3, 4, .elaboration⟩ represents ⇓(π₃, π₄) ∈ F(π₀) (using .elaboration as a stand-in for ⇓; both subordinating).
      • ⟨4, 1, 2, .background⟩ represents Background(π₁, π₂) ∈ F(π₄).

      Plus container-marking edges so that iOutscopes recovers the box-containment structure:

      • π₀ contains π₃ and π₄
      • π₄ contains π₁ and π₂

      These containment relations are conjuncts in the parent box's F-content (the book's "labels A and labelling F" representation — being a label inside a box IS a content fact about the parent). We encode them as additional outscoping conjuncts using the same edge structure.

      For Example (21) specifically, the ⇓(π₃, π₄) and Background(π₁, π₂) edges already encode the containment (since these relations have π₃, π₄, π₁, π₂ as arguments and the relations themselves live in F(π₀) and F(π₄) respectively). No additional outscoping edges needed.

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        theorem Studies.Anaphora.AsherLascarides2003.pi_1_not_available_from_pi_2 :
        ¬1 ∈ Discourse.SDRT.availableAttachmentPoints example21

        Book p. 149 headline claim: π₁ is NOT in the available attachment set from π₂ (Example 21).

        The reason: π₁ and π₂ are siblings under Background, which is coordinating (not subordinating). RFC's condition 2b only opens up new attachment sites via subordinating relations, so the sibling-via-coordinating π₁ is unreachable from π₂'s right frontier.

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        theorem Studies.Anaphora.AsherLascarides2003.available_attachment_points_match :
        Discourse.SDRT.availableAttachmentPoints example21 = [0, 2, 3, 4]

        The full available set from π₂ matches the book's prediction: {π₀, π₂, π₃, π₄}.