“on the premise that”是法律文件中经常遇见的常用搭配，通常可译为“前提是，以......为前提”,或者根据上下文及句意加以变通，以便译文准确通顺。

相关例句如下，可供参考：

The IEA operates on the premise that it is in the interest of all consuming countries to make as much oil as possible available on the world market and for countries to cooperate in the event of supply disruptions, whether due to natural or man-made crises.

国际能源署的运作理念是，力图扩大国际市场上的石油资源，各国携手合作以防石油供给由于自然或人为原因中断，这符合所有消费国的利益。

Will the Government consider releasing these green belts for the production of more public housing on the premise that no disruption to the ecology will be caused?

政府有否考虑在不妨碍自然生态发展的前提下，把这些绿化地带释放出来，使之适宜兴建更多公营房屋？ 

The AA’s investment objective is on the premise that there will be direct and indirect benefits to the airport in terms of increased commercial activities and air passenger volume.

机管局的投资目标基于一个大前提，就是新展览中心会令商业活动和航空旅客量有所增加，为机场带来直接和间接利益。