Table 6: CP semantics in LTL (subscripts C and E stand for condition and event, resp.).

CP Class Semantics in LTL

(1) AtLeastOneC 𝑃 1 𝑃 2 𝑃 𝑛
(2) AtLeastOneE ( ¬ 𝑃 1 ¬ 𝑃 𝑛 ) ( ( ¬ 𝑃 1 ¬ 𝑃 𝑛 ) 𝑈 ( 𝑃 1 𝑃 𝑛 ) )
(3) ParallelC 𝑃 1 𝑃 2 𝑃 𝑛
(4) ParallelE ( ¬ 𝑃 1 ¬ 𝑃 2 ¬ 𝑃 𝑛 ) ( ( ¬ 𝑃 1 ¬ 𝑃 2 ¬ 𝑃 𝑛 ) 𝑈 ( 𝑃 1 𝑃 2 𝑃 𝑛 ) )
(5) ConsecutiveC 𝑃 1 𝑋 ( 𝑃 2 𝑋 ( 𝑋 ( 𝑃 𝑛 ) ) ) ) )
(6) ConsecutiveE ( ¬ 𝑃 1 ¬ 𝑃 2 ¬ 𝑃 𝑛 ) ( ( ¬ 𝑃 1 ¬ 𝑃 2 ¬ 𝑃 𝑛 ) 𝑈 ( ( 𝑃 1 ¬ 𝑃 2 ¬ 𝑃 3 ¬ 𝑃 𝑛 ) 𝑋 ( ( 𝑃 2 ¬ 𝑃 3 ¬ 𝑃 𝑛 ) 𝑋 ( 𝑃 𝑛 ) ) )
(7) EventualC 𝑃 1 ( ¬ 𝑃 2 𝑈 ( 𝑃 2 ( ¬ 𝑃 𝑛 𝑈 𝑃 𝑛 ) ) )
(8) EventualE ( ¬ 𝑃 1 ¬ 𝑃 𝑛 ) ( ( ¬ 𝑃 1 ¬ 𝑃 𝑛 ) 𝑈 ( 𝑃 1 ( ( ¬ 𝑃 2 ¬ 𝑃 𝑛 ) 𝑈 ( 𝑃 2 ( ( 𝑃 𝑛 1 ( ¬ 𝑃 𝑛 𝑈 𝑃 𝑛 ) ) ) ) ) ) )
(9) Strict EventualC 𝑃 1 𝑋 ( ¬ 𝑃 2 𝑈 ( 𝑃 2 𝑋 ( ¬ 𝑃 𝑛 𝑈 𝑃 𝑛 ) ) )
(10) Strict EventualE ( ¬ 𝑃 1 ¬ 𝑃 𝑛 ) ( ( ¬ 𝑃 1 ¬ 𝑃 𝑛 ) 𝑈 ( 𝑃 1 ¬ 𝑃 2 ¬ 𝑃 𝑛 ( ( ¬ 𝑃 2 ¬ 𝑃 𝑛 ) 𝑈 ( 𝑃 2 ¬ 𝑃 3 ¬ 𝑃 𝑛 ( ( 𝑃 𝑛 1 ¬ 𝑃 𝑛 ( ¬ 𝑃 𝑛 𝑈 𝑃 𝑛 ) ) ) ) ) ) )