GCSRL - A Logic for Stochastic Reward Models with Timed and Untimed Behaviour

In this paper we define the logic GCSRL (generalised continuous stochastic reward logic) that provides means to reason about systems that have states which sojourn times are either greater zero, in which case this sojourn time is exponentially distributed (tangible states), or zero (vanishing states). In case of generalised stochastic Petri nets (GSPNs) and stochastic process algebras it turned out that these vanishing states can be very useful when it comes to define system behaviour. In the same way these states are useful for defining system properties using stochastic logics. We extend both the semantic model and the semantics of CSRL such that it allows to attach impulse rewards to transitions emanating from vanishing states. We show by means of a small example how model checking GCSRL formulae works.