While I by no means will require search engines catalogued by Entrigue to use any particular UX, and in fact I'd encourage experimentation, what's described here is my suggestion for many search engines.
The search control would look much like any other, but when users select an auto-completion a token would be added to the start of the control. The arrow keys could then be used to select a token. Once a token is selected delete would remove the token, enter would delete it whilst inserting it's text in the editing area, and the up/down keys would change the facet. The dropdown would be visible in the token, as would the delete button. Finally an arrow would be rendered next to the dropdown which upon clicking would insert an extra dropdown into the token to form a predicate path. Those would be navigable via shift-left/right.
What happens when you hit enter would be defined by the website.
And while Apple has done something very similar this design still has the desirable aspects of communicating exactly what aspects are being searched upon and allows users to adjust this interpretation. That's much more desirable than Google presuming to know what you mean or DuckDuckGo asking for clarification.
Particularly for entering time ranges, various casual terms (e.g. today, last week, next week) would be inserted into the possible autocompletions whilst translating dynamically into more specific searches.