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 ) ) ⋯ ) ) ) ) )