Cognos has an add months function. (At least, Cognos 10 does.) In your expression editor, on the functions tab, it's under Business Date/Time Functions. It's called _add_months. So your function would end up being something like between (_add_months(1,current_date))
You can also use the SQL Server function. You have to put those text parameters (like MM) in curly brackets. So you would end up with dateadd({MM},0,current_date)
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For the first day of the current month, in TSQL you would use:DATEADD(MONTH, DATEDIFF(MONTH, 0, GETDATE()), 0)
In Cognos, the syntax would be DATEADD({MONTH}, DATEDIFF({MONTH}, 0, GETDATE()), 0)