Table 4: Prospec's new LTL formulas.

Pattern Scope LTL Formula

Absence After 𝐿 ¬ ( ( ¬ 𝐿 ) 𝑈 ( 𝐿 𝑃 ) )
After 𝐿 Until 𝑅 [ ] ( 𝐿 ¬ ( 𝑅 ) ¬ ( ¬ ( 𝑅 ) 𝑈 𝑃 ) )

Existence Before 𝑅 ¬ ( ( ¬ 𝑃 ) 𝑈 𝑅 )
After 𝐿 ¬ ( ( ¬ 𝐿 ) 𝑈 ( 𝐿 ¬ 𝑃 ) )
Between 𝐿 and 𝑅 [ ] ( ( 𝐿 ¬ 𝑅 ) ( ¬ ( ( ¬ 𝑃 ) 𝑈 𝑅 ) ) )

Universality After 𝐿 ¬ ( ( ¬ 𝐿 ) 𝑈 ( 𝐿 ¬ 𝑃 ) )
After 𝐿 Until 𝑅 [ ] ( ( 𝐿 ¬ 𝑅 ) ( ¬ ( ( 𝑃 ¬ 𝑅 ) 𝑈 ( ( ¬ 𝑃 ) ¬ 𝑅 ) ) ) )

Precedence Global ¬ ( ( ¬ 𝑇 ) 𝑈 ( 𝑃 ¬ 𝑇 ) )
After 𝐿 ¬ ( ( ¬ 𝐿 ) 𝑈 ( 𝐿 ( ( ¬ 𝑇 ) 𝑈 ( 𝑃 ¬ 𝑇 ) ) ) )
After 𝐿 Until 𝑅 [ ] ( ( 𝐿 ¬ 𝑅 ) ( ¬ ( ( ( ¬ 𝑇 ) ¬ 𝑅 ) 𝑈 ( 𝑃 ( ¬ 𝑇 ) ¬ 𝑅 ) ) )

Response Before 𝑅 ¬ ( ( ¬ 𝑅 ) 𝑈 ( 𝑃 ( ¬ 𝑅 ) ( ( ¬ 𝑇 ) 𝑈 𝑅 ) ) )
After 𝐿 ¬ ( ( ¬ 𝐿 ) 𝑈 ( 𝐿 ( ¬ [ ] ( 𝑃 𝑇 ) ) ) )
Between 𝐿 and 𝑅 [ ] ( ( 𝐿 ¬ 𝑅 ) ¬ ( ( ¬ 𝑅 ) 𝑈 ( 𝑃 ( ¬ 𝑅 ) ( ( ¬ 𝑇 ) 𝑈 𝑅 ) ) ) )
After 𝐿 Until 𝑅 [ ] ( ( 𝐿 ¬ 𝑅 ) ¬ ( ( ¬ 𝑅 ) 𝑈 ( 𝑃 ( ¬ 𝑅 ) ( ( [ ] ( ( ¬ 𝑇 ) ¬ 𝑅 ) ) ( ( ¬ 𝑇 ) 𝑈 𝑅 ) ) ) ) ) )

Strict Precedence Global ¬ ( ( ¬ ( 𝑇 ¬ 𝑃 ) ) 𝑈 𝑃 ) )
After 𝐿 ¬ ( ( ¬ 𝐿 ) 𝑈 ( 𝐿 ( ( ¬ ( 𝑇 ¬ 𝑃 ) ) 𝑈 𝑃 ) ) )
Between 𝐿 and 𝑅 [ ] ( ( 𝐿 ¬ 𝑅 ) ( ¬ ( ( ( ¬ ( 𝑇 ¬ 𝑃 ) ) ¬ 𝑅 ) 𝑈 ( 𝑃 ( ¬ ( 𝑇 ¬ 𝑃 ) ) ( ¬ 𝑅 ) 𝑅 ) ) ) )
After L Until 𝑅 ¬ ( 𝐿 ( ¬ 𝑅 ) ( ( ( ¬ 𝑇 ) ¬ 𝑅 ) 𝑈 ( 𝑃 ¬ 𝑅 ) ) )