As long as you're human, you don't have a substantially different notion of trust than I do. It's part of human psychology. We had to evolve it as social beings. I've seen very ad hoc CS papers on "trust", though, which IMHO were based on nothing but fantasy. Perhaps you had one of those re-definitions in mind. I tried to contribute to this pointless literature myself for a while until I realized that it's completely fictitious. All you can say from a mathematical perspective is that trust builds up very slowly based on a numerous factors and, if betrayed, goes down very fast and stays there. However, the notion doesn't have enough substance for a fruitful non-psychological modeling; there is just not enough ideal rationality behind it.