A logic to reason about likelihood

We present a logic LL which uses a modal operator L to help capture the notion of likely. Despite the fact that no use is made of numbers, LL can capture many of the properties of likelihood in an intuitively appealing way. Using standard techniques of modal logic, we give a complete axiomatization for LL and show that satisfiability of LL formulas can be decided in exponential time. We discuss how the logic might be used in areas where decision making is crucial, such as management and medical diagnosis, and conclude by using LL to give a formal proof of correctness of a protocol for exchanging secrets.