Table 10

Hidden predicates, hard constraints, and formula templates used for bridging antecedent selection. a1, a2, a3 represent bridging anaphors, A the set of bridging anaphors in the whole document, e the antecedent candidate, Ea the set of the antecedent candidates for a according to a’s discourse scope, and E the set of antecedent candidates in the whole document.

 Hidden predicates p1 isBridging(a1, e) p2 hasSameAntecedent(a1, a2) Hard Constraints f1 ∀a ∈ A: |e ∈ E: isBridging(a, e)| ≤ 1 f2 ∀a ∈ A ∀e ∈ E: hasPairDistance(e, a, d) ∧ d < 0 → ¬isBridging(a, e) f3 ∀a1, a2 ∈ A: a1 ≠ a2 ∧ hasSameAntecedent(a1, a2) → hasSameAntecedent(a2, a1) f4 ∀a1, a2, a3 ∈ A: a1 ≠ a2 ∧ a1 ≠ a3 ∧ a2 ≠ a3 ∧ hasSameAntecedent(a1, a2) ∧ hasSameAntecedent(a2, a3) → hasSameAntecedent(a1, a3) f5 ∀a1, a2 ∈ A ∀i ∈ E: a1 ≠ a2 ∧ hasSameAntecedent(a1, a2) ∧ isBridging(a1, e) → isBridging(a2, e) f6 ∀a1, a2 ∈ A ∀e ∈ E: a1 ≠ a2 ∧ isBridging(a1, e) ∧ isBridging(a2, e) → hasSameAntecedent(a1, a2) Formula template for sibling anaphors clustering fc ∀a1, a2 ∈ A: siblingAnaphorsClusteringFormula_Template (a1, a2) → hasSameAntecedent(a1, a2) Formula template for bridging antecedent selection fr1 ∀a ∈ A ∀e ∈ E: bridgingAnaResolutionFormula_Template1 (a, e) → isBridging(a, e) fr2 ∀a ∈ A ∀e ∈ Ea: bridgingAnaResolutionFormula_Template2 (a, e) → isBridging(a, e)
 Hidden predicates p1 isBridging(a1, e) p2 hasSameAntecedent(a1, a2) Hard Constraints f1 ∀a ∈ A: |e ∈ E: isBridging(a, e)| ≤ 1 f2 ∀a ∈ A ∀e ∈ E: hasPairDistance(e, a, d) ∧ d < 0 → ¬isBridging(a, e) f3 ∀a1, a2 ∈ A: a1 ≠ a2 ∧ hasSameAntecedent(a1, a2) → hasSameAntecedent(a2, a1) f4 ∀a1, a2, a3 ∈ A: a1 ≠ a2 ∧ a1 ≠ a3 ∧ a2 ≠ a3 ∧ hasSameAntecedent(a1, a2) ∧ hasSameAntecedent(a2, a3) → hasSameAntecedent(a1, a3) f5 ∀a1, a2 ∈ A ∀i ∈ E: a1 ≠ a2 ∧ hasSameAntecedent(a1, a2) ∧ isBridging(a1, e) → isBridging(a2, e) f6 ∀a1, a2 ∈ A ∀e ∈ E: a1 ≠ a2 ∧ isBridging(a1, e) ∧ isBridging(a2, e) → hasSameAntecedent(a1, a2) Formula template for sibling anaphors clustering fc ∀a1, a2 ∈ A: siblingAnaphorsClusteringFormula_Template (a1, a2) → hasSameAntecedent(a1, a2) Formula template for bridging antecedent selection fr1 ∀a ∈ A ∀e ∈ E: bridgingAnaResolutionFormula_Template1 (a, e) → isBridging(a, e) fr2 ∀a ∈ A ∀e ∈ Ea: bridgingAnaResolutionFormula_Template2 (a, e) → isBridging(a, e)
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