▁This ▁fragment ▁is ▁often ▁preferred ▁to ▁M TL ▁because ▁some ▁problems ▁that ▁are ▁und ec id able ▁for ▁M TL ▁become ▁decid able ▁for ▁M IT L . ▁ ▁Definition ▁ ▁A ▁M IT L ▁formula ▁is ▁an ▁M TL ▁formula , ▁such ▁that ▁each ▁set ▁of ▁re als ▁used ▁in ▁sub script ▁are ▁intervals , ▁which ▁are ▁not ▁sing let ons , ▁and ▁whose ▁bounds ▁are ▁either ▁a ▁natural ▁number ▁or ▁are ▁infinite . ▁ ▁D ifference ▁from ▁M TL ▁ ▁M TL ▁can ▁express ▁a ▁statement ▁such ▁as ▁the ▁sentence ▁S : ▁" P ▁ho led ▁exactly ▁ten ▁time ▁units ▁ago ". ▁This ▁is ▁impossible ▁in ▁M IT L . ▁Instead , ▁M IT L ▁can ▁say ▁T : ▁" P ▁ho led ▁between ▁ 9 ▁and ▁ 1 0 ▁time ▁units ▁ago ". ▁Since ▁M IT L ▁can ▁express ▁T ▁but ▁not ▁S , ▁in ▁a ▁sense , ▁M IT L ▁is ▁a ▁restriction ▁of ▁M TL ▁which ▁allows ▁only ▁less ▁precise ▁statements . ▁ ▁Problem s ▁that ▁M IT L ▁avoid s ▁ ▁One ▁reason ▁to ▁want ▁to ▁avoid ▁a ▁statement ▁such ▁as ▁S ▁is ▁that ▁its ▁truth ▁value ▁may ▁change ▁an ▁arbitrary ▁number ▁of ▁times ▁in ▁a ▁single ▁time ▁unit . ▁Indeed , ▁the ▁truth ▁value ▁of ▁this ▁statement ▁may ▁change ▁as ▁many ▁times ▁as ▁the ▁truth ▁value ▁of ▁P ▁change , ▁and ▁P ▁itself ▁may ▁change ▁an ▁arbitrary ▁number ▁of ▁time ▁in ▁a ▁single ▁time ▁unit . ▁ ▁Let ▁us ▁now ▁consider ▁a ▁system , ▁such ▁as