▁it ▁must ▁recall ▁at ▁most ▁ 1 0 ▁time ▁units ▁when ▁T ▁becomes ▁true . ▁And ▁hence ▁ 1 1 ▁times ▁when ▁T ▁becomes ▁false . ▁Thus ▁this ▁system ▁must ▁recall ▁at ▁most ▁ 2 1 ▁events , ▁and ▁hence ▁can ▁be ▁implemented ▁as ▁a ▁tim ed ▁automat on ▁or ▁a ▁signal ▁automat on . ▁ ▁Ex amples ▁ ▁Ex amples ▁of ▁M IT L ▁formulas : ▁▁▁ ▁states ▁that ▁there ▁the ▁letter ▁ ▁appears ▁at ▁least ▁one ▁in ▁each ▁open ▁interval ▁of ▁length ▁ 1 . ▁▁ ▁where ▁ ▁is ▁the ▁prop he cy ▁operator ▁defined ▁as ▁ ▁and ▁which ▁states ▁that ▁the ▁first ▁occurrence ▁of ▁ ▁in ▁the ▁future ▁is ▁in ▁ ▁time ▁unit . ▁▁ ▁states ▁that ▁ ▁holds ▁exactly ▁at ▁each ▁integral ▁time ▁and ▁not ▁any time ▁else . ▁ ▁F rag ments ▁ ▁Saf ety - MT L 0 , ∞ ▁The ▁fragment ▁Saf ety - MT L 0 , v ▁is ▁defined ▁as ▁the ▁subset ▁of ▁M IT L 0 , ∞ ▁containing ▁only ▁formulas ▁in ▁positive ▁normal ▁form ▁where ▁the ▁interval ▁of ▁every ▁until ▁operator ▁has ▁an ▁upper ▁bound . ▁For ▁example , ▁the ▁formula ▁ ▁which ▁states ▁that ▁each ▁ ▁is ▁followed , ▁less ▁than ▁one ▁time ▁unit ▁later , ▁by ▁a ▁, ▁belongs ▁to ▁this ▁logic . ▁ ▁Open ▁and ▁closed ▁M IT L ▁ ▁The ▁fragment ▁Open - MT L ▁contains ▁the ▁formula ▁in ▁positive ▁normal ▁form ▁such ▁that : ▁▁ ▁for ▁each ▁, ▁ ▁is ▁open , ▁and ▁ ▁for ▁each ▁,