this will work if database was cleanly shutdown:

startup mount

then issue the following command for redo log groups that have been archived,
alter database clear logfile group X;

where X is the number of group

For redo log groups that have NOT been archived

alter database clear unarchived logfile group X;

where X is the number of group

Alternatively you could try to recreate a controlfile with TO TRACE option and edit the output file, in statement NORESETLOGS change it to RESETLOGS this will let you to open the database with RESETLOGS option

I wouyld try the first option first, make sure you havr a backup before doing these procedures.

If the database was not cleanly shutdown the situation is more complicated! You would probably need to restore a backup and apply archived logs but since you said you lost these too.... You would lose data!