Refactoring Logger interface to open and close logs
NullLogger wouldn't really need any parameters passed to 
  openLog() where as SysLogLogger would probably need some 
  parameters passed. How would I accomplish this?


Pass these parameters to the constructor, store in a private field and use it in the openLog (or any other) function.

If you use func_get_args() you wouldn't be able to replace the logging system without modifying the client code.

SLF4J is a great example for a logging framework. Check it's Logger interface. It contains some methods but none of them depend on any implementation. Logback, Log4j, JCL and other implementations implements this simple interface and their external configuration determines the details.

A note: maybe timestamp shouldn't be passed to the log function, it should be the internal of the logger implementation.