Hi dr,
Let's say you want to check if something called "Property1" is defined.
On your Admin Form or Site Form (when the content is stored) add a radio field called "Property1 defined?" with options "Yes=1" 'No=0". Default value of "0"
Now, add a conditional state on this radio field that makes the field "Is filled by" "1" when "Property1" is "filled" - see the attached manual if you aren't familiar with this. You can add this radio field in a "hidden" position so the user doesn't see it.
Now add your content items. When you enter a value for "Property1" it will change the radio field to have "Yes" selected.
Then, on your search form, include the radio field. This should solve your issue.
_jrmo