Diagnosability is a procedure whose goal is to determine whether any failure - or a class of failures - can be determined in finite time after its occurrence. Earlier works on diagnosability of discrete event systems (DES) establish some intermediary models from the analyzed model and then call some procedures to check diagnosablity based on these models, while recent works try to give a diagnosability formulation as a model- checking problem. However, there still lacks a single framework able to handle both of the diagnosability issues: how to model the problem? and how to decide it? In this paper, we build on some existing works which have formally established necessary and sufficient conditions for diagnosability of DES and we propose a generic operative formulation of diagnosability using the Œ-calculus logic, which allows resolving the diagnosability issue within a single formalism.