Editing Linear temporal logic (section)

==Relations with other logics==
LTL can be shown to be equivalent to the [[monadic first-order logic of order]], FO[<]&mdash;a result known as [[Kamp's theorem]]&mdash;<ref>{{cite book|url=https://books.google.com/books?id=TLpcI2axv8kC&pg=PA22 |title=Automata, Languages and Programming: 37th International Colloquium, ICALP ... - Google Books |date=2010-06-30 |access-date=2014-07-30|isbn=9783642141614 |last1=Abramsky |first1=Samson |author1link = Samson Abramsky|last2=Gavoille |first2=Cyril |last3=Kirchner |first3=Claude |last4=Spirakis |first4=Paul |publisher=Springer }}</ref> or equivalently to [[star-free language]]s.<ref>{{cite book|editor1=[[Orna Grumberg]] |editor2=[[Helmut Veith]] |title=25 years of model checking: history, achievements, perspectives|year=2008|publisher=Springer|isbn=978-3-540-69849-4|chapter=From [[Alonzo Church|Church]] and Prior to [[Property Specification Language|PSL]]|author=Moshe Y. Vardi|author-link=Moshe Y. Vardi }} [http://www.cs.rice.edu/~vardi/papers/25mc.ps.gz preprint]</ref>

[[Computation tree logic]] (CTL) and linear temporal logic (LTL) are both a subset of [[CTL*]], but are incomparable. For example,
* No formula in CTL can define the language that is defined by the LTL formula '''F'''('''G''' p).
*No formula in LTL can define the language that is defined by the CTL formulas '''AG'''( p → ('''EX'''q ∧ '''EX'''¬q) ) or  '''AG'''('''EF'''(p)).