Contextual logic CoL is specified through an inference system which takes into account the context of reasoning, i.e. all given facts whatsoever. That is to say, conclusions are inferred with respect to the full set of premises. Hence, statements are relative to a context and they are expressed by means of formulas indexed with sets of formulas. A modal extension ECoL is also proposed for which examples are given that illustrate how natural it is to apply such a logic for the formalization of non-monotonic reasoning.