Table 1: 

Natural logic relations (NatOps) and their set theoretic definitions.

NatOP: NameDefinition
⥮: Alternation xy = ⊘ ∧ xyU 
 ⌣ : Cover xy ≠ ⊘ ∧ xy = U 
≡: Equivalence x = y 
: Forward Entailment xy 
: Negation xy = ⊘ ∧ xy = U 
: Reverse Entailment xy 
⋕: Independence All other cases 
NatOP: NameDefinition
⥮: Alternation xy = ⊘ ∧ xyU 
 ⌣ : Cover xy ≠ ⊘ ∧ xy = U 
≡: Equivalence x = y 
: Forward Entailment xy 
: Negation xy = ⊘ ∧ xy = U 
: Reverse Entailment xy 
⋕: Independence All other cases 
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