Working out logic for Search Filters

I’m building (what will be for me) the most ambitious search functionality I’ve attempted. This would involve a text field that initially returns a set of pages, then those pages can be filtered using multiple different form elements (radio buttons, checkboxes, select fields, etc…). I’ve seen this topic covered a few times in the forum, but I’d really like to understand it from my own point of view and build it myself from scratch. Here’s how I think it would work:

Is my logic correct, or is my thinking completely wrong?