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There is a growing interest in techniques for detecting whether a logic specification is satisfied too easily, or vacuously. For example, the specification “every request is eventually followed by an acknowledgment” is satisfied vacuously by a system that never generates any requests. Vacuous satisfaction misleads users of model-checking into thinking that a system is correct. It is a serious problem in practice. There are several existing definitions of vacuity. Originally, Beer et al. [1997] formalized vacuity as insensitivity to syntactic perturbation (syntactic vacuity). This formulation captures the intuition of “vacuity” when applied to a single occurrence of a subformula. Armoni et al.

 

 

 

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