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 ) ) )