▁ ▁is ▁closed . ▁ ▁The ▁fragment ▁Cl osed - MIT L ▁contains ▁the ▁neg ation ▁of ▁formulas ▁of ▁Open - MIT L . ▁ ▁Fl at ▁and ▁C of lat ▁M IT L ▁ ▁The ▁fragment ▁Fl at - MT L ▁contains ▁the ▁formula ▁in ▁positive ▁normal ▁form ▁such ▁that : ▁▁ ▁for ▁each ▁, ▁if ▁ ▁is ▁un bounded , ▁then ▁ ▁is ▁a ▁L TL - form ula ▁ ▁for ▁each ▁, ▁if ▁ ▁is ▁un bounded , ▁then ▁ ▁is ▁a ▁L TL - form ula ▁ ▁The ▁fragment ▁C of lat - MIT L ▁contains ▁the ▁neg ation ▁of ▁formulas ▁of ▁Fl at - MIT L . ▁ ▁Non - str ict ▁variant ▁ ▁Given ▁any ▁fragment ▁L , ▁the ▁fragment ▁L ns ▁is ▁the ▁restriction ▁of ▁L ▁in ▁which ▁only ▁non ▁strict ▁operators ▁are ▁used . ▁ ▁M IT L 0 , ∞ ▁and ▁M IT L 0 ▁Given ▁any ▁fragment ▁L , ▁the ▁fragment ▁L 0 , ∞ ▁is ▁the ▁subset ▁of ▁L ▁where ▁the ▁lower ▁bound ▁of ▁each ▁interval ▁is ▁ 0 ▁or ▁the ▁upper ▁bound ▁is ▁infinity . ▁Similarly ▁we ▁denote ▁by ▁L 0 ▁( res pect ively , ▁L ∞ ) ▁the ▁subset ▁of ▁L ▁such ▁that ▁the ▁lower ▁bound ▁of ▁each ▁interval ▁is ▁ 0 ▁( res pect ively , ▁the ▁upper ▁bound ▁of ▁each ▁interval ▁is ▁ ∞ ). ▁ ▁Express iveness ▁over ▁signals ▁ ▁Over ▁signals , ▁M IT L 0 ▁is ▁as ▁express ive ▁as ▁M IT L .