Conditional chance measure and its application in hybrid logic

In this paper, a concept of conditional chance measure is first defined to measure the chance of a hybrid event after it has been learned that some other one has occurred. Furthermore, some important properties about it are proved such as the monotonicity theorem, self-duality theorem, countable subadditivity theorem and semicontinuity law. In addition, conditional chance distribution and conditional expected value are also discussed. Finally, conditional chance measure is applied to define the truth values of rules in hybrid logic, and then a hybrid modus ponens rule is proposed.