The intuitionistic temporal logic of dynamical systems

0546446 - ÚI 2022 DE eng J - Journal Article
Fernández-Duque, David
The intuitionistic temporal logic of dynamical systems.
Logical Methods in Computer Science. Roč. 14, č. 3 (2018), č. článku 3. ISSN 1860-5974. E-ISSN 1860-5974
Keywords : provability logic * intuitionistic logic * temporal logic * dynamical topological systems
Impact factor: 0.432, year: 2018

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.
Permanent Link: http://hdl.handle.net/11104/0322950