This dissertation aims to analyze the pragmatic of law-applied conversation, especially the one derived from the Gricean theory. Paul Grice has stated that comprehension in ordinary discourse results from the cooperative principle, according to which speaker and listener seek communication efficiency, and, therefore, follow certain behavior rules called conversational maxims. If the juridical activity is seen as a context-specific dialogue happening within the legal context, and if the legislator is the speaker and the judiciary and society are the listeners, then the application of the Gricean Conversation Theory, with the proviso due to the differences between ordinary and juridical discourses, is an efficient tool to seek the rationality of interpretation, through pragmatic methods, especially when the insufficiency of the methods of legal interpretation is taken into account. In a debate between the textualist and intentionalist currents, it is made clear the difficulty to measure the role of the text, the legislator`s intention, and the comprehension of the norm enforcer to, faced with the compulsoriness of the interpretative activity, explicate objective methods that avoid abuse and provide rationality and controllability to interpretation. With pragmatic interpretation and correct use of the speaker`s meaning to comprehend the best sense of the norm, each generation will be able to respond to the fundamental issue of juridical interpretation according to its own needs and values, although not ignoring a rationality pattern that provides the normative system with stability, grounded on juridical safety, and innovation, grounded on objectivity.