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== Extensions ==
CTL has been extended with second order quantifier <math>\exists p</math> and <math>\forall p</math><ref>{{Cite journal|last=David|first=Amélie|last2=Laroussinie|first2=Francois|last3=Markey|first3=Nicolas|date=2016|editor-last=Desharnais|editor-first=Josée|editor2-last=Jagadeesan|editor2-first=Radha|title=On the Expressiveness of QCTL|url=http://drops.dagstuhl.de/opus/volltexte/2016/6164|journal=27th International Conference on Concurrency Theory (CONCUR 2016)|series=Leibniz International Proceedings in Informatics (LIPIcs)|___location=Dagstuhl, Germany|publisher=Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik|volume=59|pages=28:1–28:15|doi=10.4230/LIPIcs.CONCUR.2016.28|isbn=978-3-95977-017-0}}</ref>. There are two semantics:
* the tree semantics. We label nodes of the computation tree. QCTL* = QCTL = MSO over trees. Model checking and satisfiability are tower-complete.
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