Linear temporal logic

In logic, linear temporal logic or linear-time temporal logic[1][2] (LTL) is a modal temporal logic with modalities referring to time. In LTL, one can encode formulae about the future of paths, e.g., a condition will eventually be true, a condition will be true until another fact becomes true, etc. It is a fragment of the more complex CTL*, which additionally allows branching time and quantifiers. LTL is sometimes called propositional temporal logic, abbreviated PTL.[3] In terms of expressive power, linear temporal logic (LTL) is a fragment of first-order logic.[4][5]

LTL was first proposed for the formal verification of computer programs by Amir Pnueli in 1977.[6]

  1. ^ Logic in Computer Science: Modelling and Reasoning about Systems: page 175
  2. ^ "Linear-time Temporal Logic". Archived from the original on 2017-04-30. Retrieved 2012-03-19.
  3. ^ Dov M. Gabbay; A. Kurucz; F. Wolter; M. Zakharyaschev (2003). Many-dimensional modal logics: theory and applications. Elsevier. p. 46. ISBN 978-0-444-50826-3.
  4. ^ Diekert, Volker. "First-order Definable Languages" (PDF). University of Stuttgart.
  5. ^ Kamp, Hans (1968). Tense Logic and the Theory of Linear Order (PhD). University of California Los Angeles.
  6. ^ Amir Pnueli, The temporal logic of programs. Proceedings of the 18th Annual Symposium on Foundations of Computer Science (FOCS), 1977, 46–57. doi:10.1109/SFCS.1977.32