The presidents of China and the United States will meet for an unusual, informal summit in California on June 7-8. Officials on both sides are rightly trying to lower expectations, especially for "deliverables" and detailed outcomes on some of the thorniest issues between the world's top two economies in only two days of personal diplomacy. Instead, they are stressing the opportunity for the two leaders to explore areas of cooperation and reduced competition beyond the short-term calendar.

This summit is the first in more than 40 years when the leaders of two very consequential and different powers will sit down for a "blue sky" discussion. The last was between Chairman Mao Zedong and former US president Richard Nixon in 1972. History has proved the importance of that dialogue for the principles and concepts governing Chinese and American cooperation and competition. Had they bogged themselves down in detailed disputes, which were many, beneficial strategic change would have proved elusive.

The California summit could be similarly consequential for the 21st century. Grinding competition of the sort seen recently between the two countries, potentially leading to conflict, could put them on a path to disaster. Focused cooperation, despite major systemic differences in the structure and interests of the two countries, can lead to more positive outcomes.

What should the two presidents discuss? First, presidents Xi Jinping and Barack Obama should seek to evoke from each other expressions of principle about handling the major disputes and challenges facing their countries. This is not about crafting a detailed "fourth communiqu", for which there is neither time nor need. Nor is it about creating a "G2" consortium of the US and China to lead world affairs. But if these two powers cannot work out the principles to handle many of the problems they face, regional and global cooperation may prove elusive and competition dangerous.

What are these principles? First, both leaders should state their commitment to resolve their differences and regional crises peacefully, through international law and mechanisms. Xi has repeatedly called for a "new kind of great power relationship". To Western ears, it sounds like China will not confront US global dominance. But Chinese leaders should make the concept clearer.

Second, keeping the status quo in Asia could help curb the growing frictions between China and some of its neighbors over maritime claims. Both leaders could call for further negotiations on interim arrangements to manage resource competition among the claimants over fisheries, hydrocarbons and minerals.

Third, Xi and Obama should reiterate a common commitment to denuclearization of the Korean Peninsula and ultimate peaceful reunification.