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Temporal logic
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==Temporal logics== Temporal logics include: * Some systems of [[positional logic]] * [[Linear temporal logic]] (LTL) temporal logic without branching timelines * [[Computation tree logic]] (CTL) temporal logic with branching timelines * [[Interval temporal logic]] (ITL) * [[Temporal logic of actions]] (TLA) * [[Signal temporal logic]] (STL)<ref name="autogenerated2004"/> * [[Timestamp temporal logic]] (TTL)<ref>{{Cite journal|doi=10.1145/3126510|title=Timestamp Temporal Logic (TTL) for Testing the Timing of Cyber-Physical Systems|year=2017|last1=Mehrabian|first1=Mohammadreza|last2=Khayatian|first2=Mohammad|last3=Shrivastava|first3=Aviral|last4=Eidson|first4=John C.|last5=Derler|first5=Patricia|last6=Andrade|first6=Hugo A.|last7=Li-Baboud|first7=Ya-Shian|last8=Griffor|first8=Edward|last9=Weiss|first9=Marc|last10=Stanton|first10=Kevin|journal=ACM Transactions on Embedded Computing Systems|volume=16|issue=5s|pages=1–20|s2cid=3570088|doi-access=free}}</ref> * [[Property Specification Language|Property specification language]] (PSL) * [[CTL*]], which generalizes LTL and CTL * [[Hennessy–Milner logic]] (HML) * [[Modal μ-calculus]], which includes as a subset HML and CTL* * [[Metric temporal logic]] (MTL)<ref>Koymans, R. (1990). "Specifying real-time properties with metric temporal logic", ''Real-Time Systems'' '''2'''(4): 255–299. {{doi|10.1007/BF01995674}}.</ref> * [[Metric interval temporal logic]] (MITL)<ref name="autogenerated2004">Maler, O.; Nickovic, D. (2004). "Monitoring temporal properties of continuous signals". {{doi|10.1007/978-3-540-30206-3_12}}.</ref> * [[Timed propositional temporal logic]] (TPTL) * [[Truncated Linear Temporal Logic]] (TLTL)<ref>Li, Xiao, Cristian-Ioan Vasile, and Calin Belta. "Reinforcement learning with temporal logic rewards." {{doi|10.1109/IROS.2017.8206234}}</ref> * [[Hyper temporal logic]] (HyperLTL) <ref>{{Cite book|chapter-url=https://link.springer.com/chapter/10.1007/978-3-642-54792-8_15|doi = 10.1007/978-3-642-54792-8_15|chapter = Temporal Logics for Hyperproperties|title = Principles of Security and Trust|series = Lecture Notes in Computer Science|year = 2014|last1 = Clarkson|first1 = Michael R.|last2 = Finkbeiner|first2 = Bernd|last3 = Koleini|first3 = Masoud|last4 = Micinski|first4 = Kristopher K.|last5 = Rabe|first5 = Markus N.|last6 = Sánchez|first6 = César|volume = 8414|pages = 265–284|isbn = 978-3-642-54791-1|s2cid = 8938993}}</ref> A variation, closely related to temporal or chronological or tense logics, are modal logics based upon "topology", "place", or "spatial position".<ref>{{Cite book | doi=10.1007/978-94-017-3546-9_13| chapter=Topological Logic| title=Topics in Philosophical Logic| pages=229–249| year=1968| last1=Rescher| first1=Nicholas| isbn=978-90-481-8331-9}}</ref><ref>{{Cite book |doi = 10.1007/978-94-009-9407-2_9|chapter = A Modal Logic of Place|title = The Philosophy of Nicholas Rescher|pages = 65–73|year = 1979|last1 = von Wright|first1 = Georg Henrik|isbn = 978-94-009-9409-6}}</ref>
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