Scholars from some of the nation's major think tanks yesterday proposed a new national agenda, calling for a major assault on welfare dependency, a national discussion of whether the United States possesses a common culture that its educational institutions ought to impart and a diminution of government's role in society.

The group, organized by the Hudson Institute, laid out a generally conservative program in a report delivered to President Reagan yesterday.

It calls for tax simplification, support for the "Star Wars" space-defense concept, private alternatives to Social Security and unemployment insurance, abolition of corporate income taxes, an end to the taxation of private savings and a reduction of the role of lawyers in society.

The group, the Committee on the Next Agenda, also called for greater focus on the family as the basic unit of society.

"Divorce, separation, desertion, illegitimacy -- these are the four horsemen of dependency," the report said.

The group, which included Hudson Institute chief Thomas D. Bell Jr., Roger D. Semerad of the Brookings Institution, former treasury undersecretary Norman B. Ture, Heritage Foundation President Edward J. Feulner and individuals from the Hoover Institution and the American Enterprise Institute, seeks a national commission to report on the quality of family life.

The scholars, who participated as individuals rather than spokesmen for their institutions, concluded that "concentration of power in the hands of government has undermined" individual responsibility as the force for economic progress and the family as the source of social stability.

In addition, the group of scholars said:Taxes on individuals should be revised to provide "the broadest possible income base" at the lowest, flattest possible rates and to allow broad exemptions for current savings.

The personal exemption and zero-rate bracket could be increased to provide as much progressivity in rates as desired. Wherever possible, government programs should be shifted to the private sector and government regulation removed from private life. The focus on deficits should be played down lest it undermine tax revision. Litigation and judicial lawmaking should be reduced by finding alternatives to adversarial court procedures, making federal judges subject to periodic reconfirmation and allowing non-lawyers to handle real estate settlements, divorces, wills and contracts. Family life should be strengthened by eliminating work requirements for welfare mothers with small children, removing tax provisions that discriminate against work and family cohesion, and providing tax deductions and other encouragements for adoption. A White House summit meeting on education should start a national debate to determine "what every child should learn in school."

Teacher quality should be improved through higher pay, year-round contracts, better measures of student performance and placing more emphasis on quality and less on formal education of teachers. Training policies for "hard-core unemployed youth" and functional illiterates should get public and private funding.

Tax incentives should be given for retraining and hiring displaced workers.

Employer sanctions should not be used against those who hire illegal immigrants; a better approach would be to improve border patrols.

The National Security Council should return to being a foreign policy clearinghouse, staffed largely by outside experts.

In Central America, the United States should foster democracy and provide noncommunist and democratic nations with economic, trade and military assistance, including arms and training.