If you want to change the doctype for your site, add a namespaced attribute to the html element, or do some other changes to the boilerplate text, then its quite easy.
The following adds a Facebook Open Social attribute to the html element.
Open up the functions.php file in your child theme and add the following code. The code should be entered at the end of the file, just before the closing ?> if there is one.
Alternatively, you may want to switch to the XHTML 1.0 Strict Doctype (be aware that there may be occurrences elsewhere in Genesis which uses code valid for Transitional doctype, but invalid for Strict):