Empty/unselected sections are ignored. Specified fields can be AND'ed or OR'ed while sections are always AND'ed (see search selection mode menu at bottom of page).
For example, in OR'ed search mode it is possible to search for tools which have a graphical editor AND either runs on HPs OR Linux systems (or both). Another example, in AND'ed search mode (default) it is possible to search for tools which both implements state spaces AND invariants.