On the notion of vacuous truth

  • Authors:
  • Marko Samer;Helmut Veith

  • Affiliations:
  • Department of Computer Science, Durham University, UK;Institut für Informatik, Technische Universität München, Germany

  • Venue:
  • LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
  • Year:
  • 2007

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Abstract

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.