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CTL* Semantics

This document delves into the semantics of path existence in temporal logic, particularly focusing on various modalities like eventually (AF) and always (EG) across multiple paths. It examines the implications of these modalities in determining whether certain conditions hold true under specified circumstances. Through a series of examples, such as "It always gets cloudy before it rains" and "Bad things never happen," the discussion underscores myriads of logical constructs in designing models that represent temporal behaviors consistently in both finite and infinite states.

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CTL* Semantics

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  1. CTL* Semantics CS 586

  2. E: Exists a path s NOT a model of

  3. E: Exists a path s

  4. A: All paths s NOT a model of

  5. A: All paths s

  6. F: Eventually s

  7. EF: Along some path, eventually s NOT a well-formed problem

  8. AF: Along every path, eventually s NOT a model of

  9. AF: Along every path, eventually s

  10. EGAF s there exists a path, on which it is always true that…

  11. EGAF s there exists a path, on which it is always true that… For all paths, eventually red.

  12. EGAF always means true for all states on the path. Get AF red for s. s there exists a path, on which it is always true that… For all paths, eventually red.

  13. EGAF always means true for all states on the path. Get AF red for s. s there exists a path, on which it is always true that… For all paths, eventually red.

  14. EGAF always means true for all states on the path. Get AF red for s. Get AF red for t. s there exists a path, on which it is always true that… For all paths, eventually red. t

  15. EGAF always means true for all states on the path. Get AF red for s. Get AF red for t. Get AF red for u. s there exists a path, on which it is always true that… For all paths, eventually red. t u

  16. EGAF always means true for all states on the path. Get AF red for s. Get AF red for t. Get AF red for u. Get AF red for v. s there exists a path, on which it is always true that… For all paths, eventually red. t u v

  17. s

  18. Some Examples • It always gets cloudy before it rains • Bad things never happen • Its possible to have your cake and eat it too. • I will eventually grade your homework

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