Postgres log file

I am curious about this scenario:

What is going to happen when a server is running and the Postgres log file is
accidentally deleted or renamed? The server will have no place to write its log
entries obviously.. what else?.

Is there any way to check within Postgres what the current log name (with a
particular time stamp when rotated last time) is so that a file with a correct
matching name can be manually created?

For this situation, what is the proper way to get the server to write to a new
log file without having to bounce the Postgres server itself?

Thanks!