Desktop search and privacy

["W. Martin Borgert" <debacle debian org>]

Hi,

when I type sth. in the search field in the upper right corner
of the screen, it seems that application from the menu are
searched, right? However, in certain cases, the web browser
opens and the search term is looked up in Google.

While I enjoy using Google for searching, this is sth. I want
to do on purpose and not have it implicitly when using a
naively supposed local search function. How can I change the
search function to respect my privacy and not contact any
other machines on the net?

TIA!