Abstract: On the Notion of Vacuous Truth


The model checking community has proposed numerous definitions of vacuous satisfaction, i.e., formal criteria which tell whether a temporal logic specification holds true on a system model for the intended reason. In this paper we attempt to study the notion of vacuous satisfaction from first principles. We show that despite the apparently vague formulation of the vacuity problem, most proposed notions of vacuity for temporal logic can be cast into a uniform and simple framework, and compare previous approaches to vacuity detection from this unified point of view.