Logic for search and filter

I’m trying to figure out how to get the logic right for my form.

http://ctc.warhol.org/search

Users can select checkboxes in a list of categories and in a list of tags. If they select two categories, we show everything that’s in both of the categories (so search operator is OR). But as they choose tags, I’d like to filter out the results from these categories. So if they choose tags “music” and “photography,” they get all of the music and photography stuff in the two categories above. I think this should be search operator OR as well, but then I get results for things tagged “music” and “photography” in other categories that weren’t select.

Thanks!