We present a new framework for checking safety failures. The approach is based on the conservative inference of the internal states of a system by the observation of the interaction with its environment. It is based on two similar mechanisms : forward implication, which performs the analysis of the consequences of an input applied to the system, and backward implication, that performs the same task for an output transition. While being a very simple approach, it is general and we believe it can yield efficient algorithms in different safety-failure checking problems. As a case study, we have applied this framework to an existing problem, the hazard checking in (speed-independent) asynchronous circuits. Our new methodology yields an efficient algorithm that performs better or as well as all existing algorithms, while being more general than the fastest one.