I work for an ISP and have toyed with the idea of offering a "private, no logs" VPN service. As someone running such a service, what would it take to convince you that I wasn't logging information that could be used to identify you?

(Obviously, there would be logs of some stuff -- just not the kind of things that would allow you to be individually or personally identified.)

I've read a little about zero knowledge proofs, but don't really know much about the subject to know if it could be used to verify these sorts of claims.