I presumed (that) he understood the rules.

我相信他明白这些规则。

《牛津词典》

I guarantee: I have read, understood and accepted the Rules of Global Solicitation for Shenzhen City Logo Design, and undertake that the information provided with above is true.

我承诺：我阅读、理解并接受《深圳城市形象标识全球征集规则公告》，保证所填事项属实。

youdao