Editing Linear temporal logic (section)

==Syntax==
LTL is built up from a finite set of [[propositional variable]]s ''AP'', the [[logical connective|logical operators]] ¬ and ∨, and the [[Temporal logic|temporal]] [[modal operator]]s '''X''' (some literature uses '''O''' or '''N''') and '''U'''. 
Formally, the set of LTL formulas over ''AP'' is inductively defined as follows:
* if {{math|''p'' ∈ ''AP''}} then ''p'' is an LTL formula;
* if {{mvar|ψ}} and {{mvar|φ}} are LTL formulas then {{math|¬{{var|ψ}}, {{var|φ}} ∨ {{var|ψ}}, '''X''' {{var|ψ}}}}, and {{math|{{var|φ}} '''U''' {{var|ψ}}}} are LTL formulas.<ref>Sec. 5.1 of [[Christel Baier]] and [[Joost-Pieter Katoen]], ''[[Principles of Model Checking]]'', MIT Press {{cite web|url=http://mitpress.mit.edu/catalog/item/default.asp?tid%3D11481%26ttype%3D2 |title=Principles of Model Checking - the MIT Press |access-date=2011-05-17 |url-status=dead |archive-url=https://web.archive.org/web/20101204043002/http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=11481 |archive-date=2010-12-04 }}</ref>

'''X''' is read as ne'''x'''t and '''U''' is read as '''u'''ntil.
Other than these fundamental operators, there are additional logical and temporal operators defined in terms of the fundamental operators, in order to write LTL formulas succinctly.
The additional logical operators are ∧, →, ↔, '''true''', and '''false'''.
Following are the additional temporal operators.

* '''G''' for always ('''g'''lobally)
* '''F''' for '''f'''inally
* '''R''' for '''r'''elease
* '''W''' for '''w'''eak until
* '''M''' for '''m'''ighty release