The local versions of the logs should be cumulative from test cycle to test cycle. Each local log pertains to a single test and is stored next to that test. They form a history of the execution of that test. Global logs should be reinitialized at every test cycle, and include information about all of the tests. Suite logs are accessible and readable.
Logs ought to be both machine readable and human readable.
I also recommend that they be tied into an icon or some other convenient front end so that they are easy to get to. Tests can be selectively activated or deactivated. This is useful for when a test reveals a crash bug, and there is no reason to run it again until the bug is fixed. Tests are easily reconfigured, replicated, or modified. An example of this is a functional test of a program with a graphical user interface that can be configured to simulate either mouse input or keyboard input.