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Table 5 

Hidden predicates and formulas used for bridging anaphora recognition. m represents a mention, M the set of mentions in the whole document, s an IS class, S the set of eight IS classes, and w the weight learned from the data for the specific formula.

Hidden predicates 
phasIS(m, s
Formulas 
Hard constraints 
fmM: |sS: hasIS(m, s)| = 1 
  
Joint inference formula template 
fg (w) ∀mi, mjMsmi,smjS: jointInferenceFormula_Constraint (mi, mj) → hasIS(mi, smi) ∧ hasIS(mj, smj
  
Non-joint inference formula template 
fl (w) ∀mMsS: non-jointInferenceFormula_Constraint (m, s) → hasIS(m, s
Hidden predicates 
phasIS(m, s
Formulas 
Hard constraints 
fmM: |sS: hasIS(m, s)| = 1 
  
Joint inference formula template 
fg (w) ∀mi, mjMsmi,smjS: jointInferenceFormula_Constraint (mi, mj) → hasIS(mi, smi) ∧ hasIS(mj, smj
  
Non-joint inference formula template 
fl (w) ∀mMsS: non-jointInferenceFormula_Constraint (m, s) → hasIS(m, s
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