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SYNTAX


LTL is built up from a set of Proposition Variable s p_1, p_2, ..., the usual logic connectives
eg,\or,\and, ightarrow and the following Temporal Modal Operator s:

  • N for next;

  • G for always;

  • F for eventually;

  • U for until;

  • R for release.


The first three operators are unary, so that N \phi is a Well-formed Formula whenever \phi is a well-formed formula. The last two operators are binary, so that \phi '''U''' \psi is a well-formed formula whenever \phi and \psi are well-formed formulas.


SEMANTICS


An LTL formula can be evaluated over a sequence of truth evaluations and a position on that path. An LTL formula is satisfied by a path if and only if it is satisfied for position 0 on that path. The semantics for the modal operators is given as follows.

One can reduce to two of those operators since the following is always satisfied:
  • F \phi = '''true''' '''U''' \phi

  • G \phi =

    • eg F

eg\phi
  • \phiR\psi =

    • eg(

eg\phiU
eg\psi)

LTL can be shown to be equivalent to the First-order Logic over one successor and the smaller Relation , FO {Link without Title} as well as Star-free Regular Expression s or Deterministic Finite Automata with Loop Complexity 0.


RELATIONS WITH OTHER LOGICS


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SEE ALSO



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