There's a reason you don't often see phrases like, "Can't prove a negative," used by people whose job is to evaluate security risks. The relevant way of approaching problems like these tends to use a lot less Boole and a lot more Bayes.
So, same question, and this time really think about it: you are capable of keeping an eye on a limited number of potential threats, you can never completely disprove that any individual means you harm, but you have to look as carefully as you can at the most plausible threats in the time you have available. How suspicious is my behavior, and what evidence would it take to convince you that my threat is negligible? What about the idea that you might personally be blamed if you cleared me and I later turned out to be a terrorist: does that affect your calculations? If so, is that in the best interests of the airport, or just you personally?
So, same question, and this time really think about it: you are capable of keeping an eye on a limited number of potential threats, you can never completely disprove that any individual means you harm, but you have to look as carefully as you can at the most plausible threats in the time you have available. How suspicious is my behavior, and what evidence would it take to convince you that my threat is negligible? What about the idea that you might personally be blamed if you cleared me and I later turned out to be a terrorist: does that affect your calculations? If so, is that in the best interests of the airport, or just you personally?