Table 3: Prospec's original LTL formulas for pattern and scope.
Pattern Scope LTL Formula
Absence Global ¬ ( ⋄ 𝑃 )
Before 𝑅 ⋄ 𝑅 → ¬ ( ¬ ( 𝑅 ) 𝑈 𝑃 )
After 𝐿 ¬ ( 𝐿 ) 𝑊 ( 𝐿 ∧ ¬ ( ⋄ 𝑃 ) )
Between 𝐿 and 𝑅 [ ] ( ( 𝐿 ∧ ¬ ( 𝑅 ) ∧ ⋄ 𝑅 ) → ¬ ( ¬ ( 𝑅 ) 𝑈 𝑃 ) )
After 𝐿 Until 𝑅 [ ] ( 𝐿 ∧ ¬ ( 𝑅 ) → ¬ ( ¬ ( 𝑅 ) 𝑈 𝑃 ) )
Existence Global ( ⋄ 𝑃 )
Before 𝑅 ⋄ 𝑅 → ( ¬ ( 𝑅 ) 𝑈 ( 𝑃 ∧ ¬ ( 𝑅 ) ) )
After 𝐿 ¬ ( 𝐿 ) 𝑊 ( 𝐿 ∧ ( ⋄ 𝑃 ) )
Between 𝐿 and 𝑅 [ ] ( ( 𝐿 ∧ ¬ ( 𝑅 ) ∧ ⋄ 𝑅 ) → ( ¬ ( 𝑅 ) 𝑈 ( 𝑃 ∧ ¬ ( 𝑅 ) ) ) )
After 𝐿 Until 𝑅 [ ] ( ( 𝐿 ∧ ¬ ( 𝑅 ) ) → ( ¬ ( 𝑅 ) 𝑈 ( 𝑃 ∧ ¬ ( 𝑅 ) ) ) )
Universality Global [ ] 𝑃
Before 𝑅 ⋄ 𝑅 → ( 𝑃 𝑈 𝑅 )
After 𝐿 ¬ ( 𝐿 ) 𝑊 ( 𝐿 ∧ [ ] 𝑃 )
Between 𝐿 and 𝑅 [ ] ( ( 𝐿 ∧ ¬ ( 𝑅 ) ∧ ⋄ 𝑅 ) → ( 𝑃 𝑈 𝑅 ) )
After 𝐿 Until 𝑅 [ ] ( ( 𝐿 ∧ ¬ ( 𝑅 ) ) → ( 𝑃 𝑊 𝑅 ) )
Precedence Global ¬ ( 𝑃 ) 𝑊 𝑇
Before 𝑅 ⋄ 𝑅 → ( ¬ ( 𝑃 ) 𝑈 ( 𝑇 ∨ 𝑅 ) )
After 𝐿 ¬ ( 𝐿 ) 𝑊 ( 𝐿 ∧ ( ¬ ( 𝑃 ) 𝑊 ( 𝑇 ) ) )
Between 𝐿 and 𝑅 [ ] ( ( 𝐿 ∧ ¬ ( 𝑅 ) ∧ ⋄ 𝑅 ) → ( ¬ ( 𝑃 ) 𝑈 ( ( 𝑇 ∨ 𝑅 ) ) ) )
After 𝐿 Until 𝑅 [ ] ( 𝐿 ∧ ¬ ( 𝑅 ) → ( ¬ ( 𝑃 ) 𝑊 ( 𝑇 ∨ 𝑅 ) ) )
Response Global [ ] ( 𝑃 → ⋄ 𝑇 )
Before 𝑅 ⋄ 𝑅 → ( ( 𝑃 → ( ¬ ( 𝑅 ) 𝑈 ( 𝑇 ∧ ¬ ( 𝑅 ) ) ) ) 𝑈 𝑅 )
After 𝐿 ( ¬ 𝐿 ) 𝑊 ( 𝐿 ∧ [ ] ( 𝑃 → ⋄ 𝑇 ) )
Between 𝐿 and 𝑅 [ ] ( ( 𝐿 ∧ ¬ ( 𝑅 ) ∧ ⋄ 𝑅 ) → ( 𝑃 → ( ¬ ( 𝑅 ) 𝑈 ( 𝑇 ∧ ¬ ( 𝑅 ) ) ) ) 𝑈 𝑅
After 𝐿 Until 𝑅 [ ] ( ( 𝐿 ∧ ¬ ( 𝑅 ) → ( 𝑃 → ( ¬ ( 𝑅 ) 𝑈 ( 𝑇 ∧ ¬ ( 𝑅 ) ) ) ) 𝑊 𝑅 )
Strict Precedence Global ¬ ( 𝑃 ) 𝑊 ( 𝑇 ∧ ¬ ( 𝑃 ) )
Before 𝑅 ⋄ 𝑅 → ( ¬ ( 𝑃 ) 𝑈 ( ( 𝑇 ∧ ¬ ( 𝑃 ) ) ∨ 𝑅 ) )
After 𝐿 ¬ ( 𝐿 ) 𝑊 ( 𝐿 ∧ ( ¬ ( 𝑃 ) 𝑊 ( 𝑇 ∧ ¬ ( 𝑃 ) ) ) )
Between 𝐿 and 𝑅 [ ] ( ( 𝐿 ∧ ¬ ( 𝑅 ) ∧ ⋄ 𝑅 ) → ( ¬ ( 𝑃 ) 𝑈 ( ( 𝑇 ∧ ¬ ( 𝑃 ) ) ∨ 𝑅 ) ) )
After 𝐿 Until 𝑅 [ ] ( 𝐿 ∧ ¬ ( 𝑅 ) → ( ¬ ( 𝑃 ) 𝑊 ( ( 𝑇 ∧ ¬ ( 𝑃 ) ) ∨ 𝑅 ) ) )