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The intuitionistic temporal logic of dynamical systems

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Abstract
A dynamical system is a pair (X, f), where X is a topological space and f : X -> X is continuous. Kremer observed that the language of propositional linear temporal logic can be interpreted over the class of dynamical systems, giving rise to a natural intuitionistic temporal logic. We introduce a variant of Kremer's logic, which we denote ITL lozenge c, and show that it is decidable. We also show that minimality and Poincare recurrence are both expressible in the language of ITL lozenge c, thus providing a decidable logic capable of reasoning about non-trivial asymptotic behavior in dynamical systems.
Keywords
intuitionistic logic, temporal logic, dynamical topological systems, PROVABILITY LOGIC

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MLA
Fernández-Duque, David. “The Intuitionistic Temporal Logic of Dynamical Systems.” LOGICAL METHODS IN COMPUTER SCIENCE, vol. 14, no. 3, 2018, doi:10.23638/LMCS-14(3:3)2018.
APA
Fernández-Duque, D. (2018). The intuitionistic temporal logic of dynamical systems. LOGICAL METHODS IN COMPUTER SCIENCE, 14(3). https://doi.org/10.23638/LMCS-14(3:3)2018
Chicago author-date
Fernández-Duque, David. 2018. “The Intuitionistic Temporal Logic of Dynamical Systems.” LOGICAL METHODS IN COMPUTER SCIENCE 14 (3). https://doi.org/10.23638/LMCS-14(3:3)2018.
Chicago author-date (all authors)
Fernández-Duque, David. 2018. “The Intuitionistic Temporal Logic of Dynamical Systems.” LOGICAL METHODS IN COMPUTER SCIENCE 14 (3). doi:10.23638/LMCS-14(3:3)2018.
Vancouver
1.
Fernández-Duque D. The intuitionistic temporal logic of dynamical systems. LOGICAL METHODS IN COMPUTER SCIENCE. 2018;14(3).
IEEE
[1]
D. Fernández-Duque, “The intuitionistic temporal logic of dynamical systems,” LOGICAL METHODS IN COMPUTER SCIENCE, vol. 14, no. 3, 2018.
@article{8603898,
  abstract     = {A dynamical system is a pair (X, f), where X is a topological space and f : X -> X is continuous. Kremer observed that the language of propositional linear temporal logic can be interpreted over the class of dynamical systems, giving rise to a natural intuitionistic temporal logic. We introduce a variant of Kremer's logic, which we denote ITL lozenge c, and show that it is decidable. We also show that minimality and Poincare recurrence are both expressible in the language of ITL lozenge c, thus providing a decidable logic capable of reasoning about non-trivial asymptotic behavior in dynamical systems.},
  articleno    = {3},
  author       = {Fernández-Duque, David},
  issn         = {1860-5974},
  journal      = {LOGICAL METHODS IN COMPUTER SCIENCE},
  keywords     = {intuitionistic logic,temporal logic,dynamical topological systems,PROVABILITY LOGIC},
  language     = {eng},
  number       = {3},
  pages        = {35},
  title        = {The intuitionistic temporal logic of dynamical systems},
  url          = {http://dx.doi.org/10.23638/LMCS-14(3:3)2018},
  volume       = {14},
  year         = {2018},
}

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