Satisfaction Up to Liveness

An approximation to the usual linear satisfaction of temporal properties is discussed in this paper. It is called satisfaction up to liveness as it only differs from the linear satisfaction relation on liveness but not on safety properties. From the point of view of observation, satisfaction up to liveness and linear satisfaction are indistinguishable. Roughly speaking, by observing all finite behaviours (exhaustive testing), we do not know whether a system satisfies a property up to liveness or linearly. Being indistinguishable from linear satisfaction in terms of complete observations, satisfaction up to liveness offers an alternative approach to model-checking.